Algebraic Surfaces and Their Moduli Spaces: Real, Differentiable and Symplectic Structures

 Access to full text

 Full (PDF)

 Full (DjVu)

1. AMOROS, J. - BOGOMOLOV, F. - KATZARKOV, L. - PANTEV, T., Symplectic Lefschetz fibrations with arbitrary fundamental group, With an appendix by Ivan Smith, J. Differential Geom., 54, no. 3 (2000), 489-545. Zbl1031.57021MR1823313
2. ANDREOTTI, A. - FRANKEL, T., The second Lefschetz theorem on hyperplane sections, in `Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo, Press, Tokyo (1969), 1-20. MR271106
3. ARTIN, E., Theorie der Zöpfe, Hamburg Univ. Math. Seminar Abhandlungen, 4-5 (1926), 47-72. MR3069440DOI10.1007/BF02950718
4. ARTIN, E., The collected papers of Emil Artin, edited by Serge Lang and John T. Tate, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London (1965). Zbl0146.00101MR176888
5. AUROUX, D. - KATZARKOV, L., Branched coverings of $C{P}^2$ and invariants of symplectic 4-manifolds, Inv. Math., 142 (2000), 631-673. Zbl0961.57019MR1804164DOI10.1007/PL00005795
6. AUROUX, D., Fiber sums of genus 2 Lefschetz fibrations, Turkish J. Math.27, no. 1 (2003), 1-10. Zbl1075.53087MR1975329
7. AUROUX, D. - DONALDSON, S. - KATZARKOV, L., Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves. Math. Ann., 326, no. 1 (2003), 185-203. Zbl1026.57020MR1981618DOI10.1007/s00208-003-0418-9
8. AUROUX, D. - DONALDSON, S. - KATZARKOV, L. - YOTOV, M., Fundamental groups of complements of plane curves and symplectic invariants, Topology, 43, no. 6 (2004), 1285-1318. Zbl1067.53069MR2081427DOI10.1016/j.top.2004.01.006
9. AUROUX, D. - KATZARKOV, L., A degree doubling formula for braid monodromies and Lefschetz pencils, arXiv:math/0605001, Pure Appl. Math. Q., 4, no. 2, part 1 (2008) 237-318. Zbl1153.57018MR2400878DOI10.4310/PAMQ.2008.v4.n2.a2
10. BARTH, W. - PETERS, C. - VAN DE VEN, A., Compact complex surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Springer-Verlag, Berlin (1984). Zbl0718.14023
11. BAUER, I. - CATANESE, F. - GRUNEWALD, F., Beauville surfaces without real structures. In: Geometric methods in algebra and number theory, Progr. Math., 235, Birkhäuser (2005), 1-42. Zbl1094.14508MR2159375DOI10.1007/0-8176-4417-2_1
12. BAUER, I. - CATANESE, F. - GRUNEWALD, F., Chebycheff and Belyi polynomials, dessins d'enfants, Beauville surfaces and group theory. Mediterranean J. Math.3, no.2 (2006) 119-143. MR2241319DOI10.1007/s00009-006-0069-7
13. BAUER, I. - CATANESE, F. - GRUNEWALD, F., The classification of surfaces with $p_g=q=0$ isogenous to a product of curves, math.AG/0610267, Pure Appl. Math. Q.4, no. 2, part 1 (2008), 547-586. Zbl1151.14027MR2400886DOI10.4310/PAMQ.2008.v4.n2.a10
14. BAUER, I. - CATANESE, F. - GRUNEWALD, F., The absolute Galois group acts faithfully on the connected components of the moduli spaces of surfaces of general type? preliminary version 2007. 
15. BIRMAN, J. S., Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo (1974). MR375281
16. BOMBIERI, E., Canonical models of surfaces of general type, Publ. Math. I.H.E.S., 42 (1973), 173-219. MR318163
17. BOMBIERI, E., The Mordell conjecture revisited, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 17, no. 4 (1990), 615-640. Zbl0722.14010MR1093712
18. CATANESE, F., Moduli of surfaces of general type. in 'Algebraic geometry-open problems' (Ravello, 1982), Lecture Notes in Math., 997, Springer, Berlin-New York (1983), 90-112. MR714742
19. CATANESE, F., On the Moduli Spaces of Surfaces of General Type, J. Differential Geom., 19 (1984), 483-515. Zbl0549.14012MR755236
20. CATANESE, F., On a problem of Chisini, Duke Math. J., 53 (1986), 33-42. Zbl0609.14031MR835794DOI10.1215/S0012-7094-86-05302-0
21. CATANESE, F., Automorphisms of Rational Double Points and Moduli Spaces of Surfaces of General Type, Comp. Math., 61 (1987), 81-102. Zbl0615.14021MR879190
22. CATANESE, F., Connected Components of Moduli Spaces, J. Differential Geom., 24 (1986), 395-399. Zbl0621.14014MR868977
23. CATANESE, F., Moduli of algebraic surfaces, Theory of moduli (Montecatini Terme, 1985), Lecture Notes in Math., 1337, Springer, Berlin (1988), 1-83. MR963062DOI10.1007/BFb0082806
24. CATANESE, F., Moduli and classification of irregular Kähler manifolds (and algebraic varieties) with Albanese general type fibrations, Invent. math., 104 (1991), 263-289. Zbl0743.32025MR1098610DOI10.1007/BF01245076
25. CATANESE, F., Fibred surfaces, varieties isogenous to a product and related moduli spaces, Amer. J. Math., 122, no. 1 (2000), 1-44. Zbl0983.14013MR1737256
26. CATANESE, F., Moduli Spaces of Surfaces and Real Structures, Ann. Math. (2), 158, no. 2 (2003), 577-592. Zbl1042.14011MR2018929DOI10.4007/annals.2003.158.577
27. CATANESE, F., Symplectic structures of algebraic surfaces and deformation, 14 pages, math.AG/0207254. 
28. CATANESE, F. - WAJNRYB, B., Diffeomorphism of simply connected algebraic surfaces, math.AG/0405299, J. Differ. Geom., 76, No. 2 (2007), 177-213. Zbl1127.14039MR2330412DOI10.4310/jdg/1180135677
29. CATANESE, F. - WAJNRYB, B., The 3-cuspidal quartic and braid monodromy of degree 4 coverings, Ciliberto, C. (ed.) et al., Projective varieties with unexpected properties. A volume in memory of Giuseppe Veronese. Proceedings of the international conference "Varieties with unexpected properties", Siena, Italy, June 8-13, 2004.Berlin: Walter de Gruyter (2005), 113-129. MR2202250
30. CATANESE, F., Canonical symplectic structures and deformations of algebraic surfaces, math.AG/0608110, Comm. Contemp. Math. (2009). Zbl1183.14046MR2538209DOI10.1142/S0219199709003478
31. CATANESE, F., Differentiable and deformation type of algebraic surfaces, real and symplectic structures. (English) Catanese, Fabrizio (ed.) et al., Symplectic 4-manifolds and algebraic surfaces. Lectures given at the C.I.M.E. summer school, Cetraro, Italy, September 2-10, 2003. Berlin: Springer; Florence: Fondazione C.I.M.E.Lecture Notes in Mathematics1938 (2008), 55-167. Zbl1145.14001MR2441412DOI10.1007/978-3-540-78279-7_2
32. CATANESE, F. - LÖNNE, M. - WAJNRYB, B., Moduli spaces and braid monodromy types of bidouble covers of the quadric, preliminary version 2008. 
33. CHISINI, O., Sulla identità birazionale delle funzioni algebriche di due variabili dotate di una medesima curva di diramazione, Ist. Lombardo Sci. Lett. Cl. Sci. Mat. Nat. Rend. (3), 8 (77) (1944), 339-356. MR19351
34. CHISINI, O., Il teorema di esistenza delle trecce algebriche. I-III, Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8), 17-18 (1954), 143-149; (1955), 307-311; (1955), 8-13. MR71103
35. DEHN, M., Die Gruppe der Abbildungsklassen. (Das arithmetische Feld auf Flächen.), Acta Math., 69 (1938), 135-206. Zbl0019.25301MR1555438DOI10.1007/BF02547712
36. DONALDSON, S. K., An Application of Gauge Theory to Four-Dimensional Topology, J. Differential Geom., 18 (1983), 279-315. Zbl0507.57010MR710056
37. DONALDSON, S. K., Connections, cohomology and the intersection forms of 4-manifolds, J. Differential Geom., 24 (1986), 275-341. Zbl0635.57007MR868974
38. DONALDSON, S. K., Polynomial invariants for smooth four-manifolds, Topology, 29, 3 (1990), 257-315. Zbl0715.57007MR1066174DOI10.1016/0040-9383(90)90001-Z
39. DONALDSON, S. K., Gauge theory and four-manifold topology. [CA] Joseph, A. (ed.) et al., First European congress of mathematics (ECM), Paris, France, July 6-10, 1992. Volume I: Invited lectures (Part 1). Basel: Birkhäuser, Prog. Math., 119 (1994), 121-151. Zbl0855.57002MR1341822
40. DONALDSON, S. K., The Seiberg-Witten Equations and 4-manifold topology. Bull. Am. Math. Soc. (N S), 33, 1 (1996), 45-70. Zbl0872.57023MR1339810DOI10.1090/S0273-0979-96-00625-8
41. DONALDSON, S. K., Symplectic submanifolds and almost-complex geometry, J. Differential Geom., 44, 4 (1996), 666-705. Zbl0883.53032MR1438190
42. DONALDSON, S. K., Lefschetz pencils on symplectic manifolds, J. Differential Geom., 53, no. 2 (1999), 205-236. Zbl1040.53094MR1802722
43. DONALDSON, S. K. - KRONHEIMER, P. B., The geometry of four-manifolds, Oxford Mathematical Monographs. Oxford: Clarendon Press (1990), ix-440. Zbl0820.57002MR1079726
44. EHRESMANN, C., Sur les espaces fibrés différentiables, C.R. Acad. Sci. Paris, 224 (1947), 1611-1612. Zbl0029.42001MR20774
45. ENRIQUES, F., Le Superficie Algebriche, Zanichelli, Bologna (1949). MR31770
46. FALTINGS, G., Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math., 73, no. 3 (1983), 349-366. MR718935DOI10.1007/BF01388432
47. FALTINGS, G., Finiteness theorems for abelian varieties over number fields', Invent. Math., 75, no. 2 (1984), 381. Zbl0602.14044MR732554DOI10.1007/BF01388572
48. FREEDMAN, M., The topology of four-dimensional manifolds, J. Differential Geom., 17, n. 3 (1982), 357-454. Zbl0528.57011MR679066
49. FREEDMAN, M. - QUINN, F., Topology of 4-manifolds, Princeton Math. Series, 39 (1990). Zbl0705.57001MR1201584
50. FRIEDMAN, R. - MOISHEZON, B. G. - MORGAN, J. W., On the $C^{\mathrm{\infty }}$ invariance of the canonical classes of certain algebraic surfaces, Bull. Amer. Math. Soc., 17 (1987), 283-286. Zbl0627.57014MR903733DOI10.1090/S0273-0979-1987-15561-3
51. FRIEDMAN, R. - MORGAN, J. W., Algebraic surfaces and four-manifolds: some conjectures and speculations, Bull. Amer. Math. Soc., 18 (1988) 1-19. Zbl0662.57016MR919651DOI10.1090/S0273-0979-1988-15576-0
52. FRIEDMAN, R. - MORGAN, J. W., Smooth four-manifolds and complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 27, Springer-Verlag, Berlin, (1994), x+520. Zbl0817.14017MR1288304DOI10.1007/978-3-662-03028-8
53. FRIEDMAN, R. - MORGAN, J. W., Algebraic surfaces and Seiberg-Witten invariants, J. Algebr. Geom., 6, No. 3 (1997) 445-479. Zbl0896.14015MR1487223
54. GIESEKER, D., Global moduli for surfaces of general type, Invent. Math., 43, no. 3 (1977), 233-282. Zbl0389.14006MR498596DOI10.1007/BF01390081
55. GOMPF, R. E., A new construction of symplectic manifolds, Ann. of Math., 142, 3 (1995), 527-595. Zbl0849.53027MR1356781DOI10.2307/2118554
56. GOMPF, R. E., The topology of symplectic manifolds, Turkish J. Math., 25, no. 1 (2001), 43-59. Zbl0989.53054MR1829078
57. GOMPF, R. E. - STIPSICZ, A., 4-manifolds and Kirby calculus, Graduate Studies in Mathematics, 20. American Mathematical Society, Providence, RI (1999) xvi+558. MR1707327DOI10.1090/gsm/020
58. GRAUERT, H., Über die Deformation isolierter Singularitäten analytischer Mengen, Invent. Math., 15 (1972), 171-198. Zbl0237.32011MR293127DOI10.1007/BF01404124
59. GRAUERT, H., Der Satz von Kuranishi für kompakte komplexe Räume, Invent. Math., 25 (1974), 107-142. MR346194DOI10.1007/BF01390171
60. GROTHENDIECK, A., Techniques de construction et théoremes d'existence en géométrie algébrique. IV, Les schemas de Hilbert, Sem. Bourbaki, Vol. 13, (1960-61), 1-28. Zbl0236.14003MR1611170
61. HATCHER, A. - THURSTON, W., A presentation for the mapping class group of a closed orientable surface, Topology, 19, no. 3 (1980), 221-237. Zbl0447.57005MR579573DOI10.1016/0040-9383(80)90009-9
62. HIRONAKA, H., Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109-203; ibid. 205-326. Zbl0122.38603MR199184
63. JOST, J. - YAU, S. T., A strong rigidity theorem for a certain class of compact complex analytic surfaces, Math. Ann., 271 (1985), 143-152. Zbl0554.32021MR779612DOI10.1007/BF01455803
64. KAS, A., On the handlebody decomposition associated to a Lefschetz fibration, Pacific J. Math., 89, no. 1 (1980), 89-104. Zbl0457.14011MR596919
65. Open problems: Classification of algebraic and analytic manifolds. Classification of algebraic and analytic manifolds, Proc. Symp. Katata/Jap. 1982. Edited by Kenji Ueno. Progress in Mathematics, 39. Birkhäuser, Boston, Mass. (1983), 591-630. MR728620
66. KHARLAMOV, V. M. - KULIKOV, V. S., On real structures of real surfaces. Izv. Ross. Akad. Nauk Ser. Mat., 66, no. 1 (2002), 133-152; translation in Izv. Math.66, no. 1 (2002), 133-150. Zbl1055.14060MR1917540DOI10.1070/IM2002v066n01ABEH000374
67. KHARLAMOV, V. - KULIKOV, V., Deformation inequivalent complex conjugated complex structures and applications, Turkish J. Math., 26, no. 1 (2002), 1-25. Zbl1047.14020MR1892797
68. KODAIRA, K. - SPENCER, D. C., On deformations of complex analytic structures. I, II, Ann. of Math. (2), 67 (1958), 328-466. Zbl0128.16901MR112154DOI10.2307/1970009
69. KODAIRA, K., On compact complex analytic surfaces, I, Ann. of Math., 71 (1960), 111-152. Zbl0098.13004MR132556DOI10.2307/1969881
70. KODAIRA, K., On compact analytic surfaces, III, Ann. Math. (2), 78 (1963), 1-40. Zbl0171.19601MR184257
71. KODAIRA, K., On the structure of compact complex analytic surfaces. I, Amer. J. Math., 86 (1964), 751-798. Zbl0137.17501MR187255DOI10.2307/2373157
72. KODAIRA, K., On the structure of compact complex analytic surfaces. II, Amer. J. Math., 88 (1966), 682-721. Zbl0193.37701MR205280DOI10.2307/2373150
73. KOLLÁR, J. - SHEPHERD BARRON, N. I., Threefolds and deformations of surface singularities, Inv. Math., 91 (1988) 299-338. Zbl0642.14008MR922803DOI10.1007/BF01389370
74. KULIKOV, V. S., On Chisini's conjecture, Izv. Ross. Akad. Nauk Ser. Mat.63, no. 6 (1999), 83-116; translation in Izv. Math., 63, no. 6 (1999), 1139-1170. MR1748562DOI10.1070/im1999v063n06ABEH000267
75. KULIKOV, V. S., On Chisini's conjecture. II, math. AG/0610356v1. Zbl1153.14012
76. KURANISHI, M., On the locally complete families of complex analytic structures, Ann. Math. (2), 75 (1962), 536-577. Zbl0106.15303MR141139DOI10.2307/1970211
77. KURANISHI, M., New proof for the existence of locally complete families of complex structures, Proc. Conf. Complex Analysis, Minneapolis, 1964 (1965), 142-154. Zbl0144.21102MR176496
78. MANDELBAUM, R. - MOISHEZON, B., On the topological structure of non-singular algebraic surfaces in $C{P}^3$, Topology, 15 (1976), 23-40. Zbl0323.57005MR405458DOI10.1016/0040-9383(76)90047-1
79. MANDELBAUM, R. - MOISHEZON, B., On the topology of simply-connected algebraic surfaces, Trans. Am. Math. Soc., 260 (1980), 195-222. Zbl0465.57014MR570786DOI10.2307/1999883
80. MANETTI, M., On some Components of the Moduli Space of Surfaces of General Type, Comp. Math., 92 (1994), 285-297. Zbl0849.14016MR1286128
81. MANETTI, M., Degenerations of Algebraic Surfaces and Applications to Moduli Problems, Tesi di Perfezionamento Scuola Normale Pisa (1996), 1-142. 
82. MANETTI, M., Iterated Double Covers and Connected Components of Moduli Spaces, Topology, 36, 3 (1997), 745-764. Zbl0889.14014MR1422433DOI10.1016/S0040-9383(96)00026-2
83. MANETTI, M., On the Moduli Space of diffeomorphic algebraic surfaces, Inv. Math., 143 (2001), 29-76. Zbl1060.14520MR1802792DOI10.1007/s002220000101
84. MILNOR, J. W., Singular points of complex hypersurfaces, Annals of Mathematics Studies61, Princeton University Press and the University of Tokyo Press (1968), 122. Zbl0184.48405MR239612
85. MOISHEZON, B., Complex surfaces and connected sums of complex projective planes, Lecture Notes in Math., 603. Springer, Berlin (1977). Zbl0392.32015MR491730
86. MOISHEZON, B., Stable branch curves and braid monodromies, Algebraic geometry, Proc. Conf., Chicago Circle 1980, Lect. Notes Math., 862 (1981), 107-192. MR644819
87. MOISHEZON, B., Algebraic surfaces and the arithmetic of braids I, in Arithmetic and geometry, Pap. dedic. I. R. Shafarevich, Vol. II: Geometry' Prog. Math., 36, Birkhäuser (1983), 199-269. Zbl0592.14012MR717613
88. MOISHEZON, B. - TEICHER, M., Finite fundamental groups, free over $Z/cZ$, for Galois covers of $C{P}^2$, Math. Ann., 293, no. 4 (1992), 749-766. Zbl0739.14003MR1176029DOI10.1007/BF01444743
89. MOISHEZON, B., The arithmetics of braids and a statement of Chisini, in 'Geometric Topology, Haifa 1992', Contemp. Math., 164, Amer. Math. Soc., Providence, RI (1994), 151-175. Zbl0837.14020MR1282761DOI10.1090/conm/164/01591
90. MORGAN, J. W.,The Seiberg-Witten equations and applications to the topology of smooth four-manifolds, Mathematical Notes, 44. Princeton Univ. Press vi (1996). Zbl0846.57001MR1367507
91. MOSER, J., On the volume elements on a manifold, Trans. Amer. Math. Soc., 120 (1965), 286-294. Zbl0141.19407MR182927DOI10.2307/1994022
92. SEGRE, B., Gli automorfismi del corpo complesso, ed un problema di Corrado Segre, Atti Acc. Naz. Lincei (8), 3 (1947), 414-420. MR26987
93. SERRE, J. P., Exemples de variétés projectives conjuguées non homéomorphes, C. R. Acad. Sci. Paris, 258 (1964), 4194-4196. Zbl0117.38003MR166197
94. THURSTON, W. P., Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc., 55, no. 2 (1976), 467-468. Zbl0324.53031MR402764DOI10.2307/2041749
95. WAJNRYB, B., A simple presentation for the mapping class group of an orientable surface, Israel J. Math., 45, no. 2-3 (1983), 157-174. Zbl0533.57002MR719117DOI10.1007/BF02774014
96. WAJNRYB, B., An elementary approach to the mapping class group of a surface, Geom. Topol., 3 (1999), 405-466. Zbl0947.57015MR1726532DOI10.2140/gt.1999.3.405
97. WALL, C. T. C., On the orthogonal groups of unimodular quadratic forms, Math. Ann., 147 (1962), 328-338. Zbl0109.03305MR138565DOI10.1007/BF01440955
98. WITTEN, E., Monopoles and Four-Manifolds, Math. Res. Lett.,1 (1994), 809-822. MR1306021DOI10.4310/MRL.1994.v1.n6.a13
99. YAU, S. T., Calabi's conjecture and some new results in algebraic geometry, Proc. Natl. Acad. Sci. USA, 74 (1977), 1798-1799. Zbl0355.32028MR451180DOI10.1073/pnas.74.5.1798
100. YAU, S. T., On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math., 31, no. 3 (1978), 339-411. MR480350DOI10.1002/cpa.3160310304