Cohomologically insignificant degenerations of algebraic varieties

 Access to full text

 Full (PDF)

1. [1] M. Artin: Some numerical criteria for contractibility of curves on algebraic surfaces. Amer. Journ. Math.84 (1962) 485-496. Zbl0105.14404MR146182
2. [2] M. Artin, G. Winters: Degenerate fibres and stable reduction of curves. Topology, 10 (1971), 373-383. Zbl0196.24403MR476756
3. [3] H. Bass: On the ubiquity of Gorenstein rings. Math. Zeitsch.82 (1963) 8-28. Zbl0112.26604MR153708
4. [4] P. Deligne: Theorie de Hodge, II. Publ. Math. de l'I.H.E.S.40 (1971) 5-58. Zbl0219.14007MR498551
5. [5] P. Deligne: Theorie de Hodge, III. Publ. Math. de l'I.H.E.S.44 (1975) 5-77. Zbl0237.14003MR498552
6. [6] PH. Griffiths: Periods of integrals on algebraic manifolds. Summary of results and discussion of open problems. Bull. A.M.S.76 (1970) 228-296. Zbl0214.19802MR258824
7. [7] PH. Griffiths, J. Harris: Principles of algebraic geometry. John Wiley & Sons. 1978. Zbl0408.14001MR507725
8. [8] PH. Griffiths, W. Schmid: Recent developments in Hodge Theory. Discrete subgroups of Lie Groups, Proc. Bombay Colloq.1973, Oxford Press, 1975, pp. 31-127. Zbl0355.14003MR419850
9. [9] Groupes de Monodromie en Geometrie Algebrique (SGA 7 I). Lect. Notes in Math. no. 288, Springer-Verlag, 1972. Zbl0237.00013
10. [10] Groupes de Monodromie en Geometrie Algebriqie (SGA 7 II). Lect. Notes in Math. no. 340, Springer-Verlag, 1973. Zbl0258.00005
11. [11] U. Karras: Deformations of cusp singularities. Proc. Symp. Pure Math., vol. XXX (1977) 37-44. Zbl0352.14007MR472811
12. [12] M. Kato, Y. Matsumoto: On the connectivity of the Milnor fiber of a holomorphic function at a critical point. Proc. Confer. Manifolds, Tokyo, 1973, pp. 131-136. Zbl0309.32008MR372880
13. [13] K. Kodaira: On compact analytic surfaces. Ann. Math.77 (1963) 563-626. Zbl0118.15802
14. [14] S. Maclane: Homology. Springer-Verlag, 1963. Zbl0133.26502
15. [15] J. Mather: Stratifications and mappings. Dynamical systems, pp. 195-233, Acad. Press.1973. Zbl0286.58003MR368064
16. [16] J. Milnor: Singular points of complex hypersurfaces. Ann. Math. Studies, 61, Princeton, 1968. Zbl0184.48405MR239612
17. [17] D. Mumford: Stability of projective varieties. L'Enseigment Math.IIe Ser., XXIII (1977) 39-110. Zbl0363.14003MR450272
18. [18] M. Raynaud: Specialization du foncteur de Picard. Publ. Math. de l'I.H.E.S., 38 (1970) 27-76. Zbl0207.51602
19. [19] M. Reid: Elliptic Gorenstein singularities of surfaces. (Preprint), 1976. 
20. [20] J. Roberts: Generic projections of algebraic varieties. Amer. Journ. Math.93 (1971) 191-214. Zbl0212.53801MR277530
21. [21] K. Saito: Einfach-elliptische Singularitaten. Inv. Math.23 (1974) 289-325. Zbl0296.14019MR354669
22. [22] W. Schmid: Variations of Hodge structures: The singularities of the period mapping. Inv. Math.22 (1973) 211-230. Zbl0278.14003MR382272
23. [23] J. Shah: Insignificant limit singularities of surfaces and their mixed Hodge structure. Ann. Math., 109 (1979) 497-536. Zbl0414.14022MR534760
24. [24] E. Spanier: Algebraic Topology. McGraw-Hill Book Co. 1966. Zbl0145.43303MR210112
25. [25] J. Steenbrink: Limits of Hodge structures. Inv. Math.31 (1976) 229-257. Zbl0303.14002MR429885
26. [26] J. Steenbrink: Mixed Hodge structure on the vanishing cohomology. Real and complex singularities, pp. 525-564, Sijthoff and Noordhoff Internat. Publ.1977. Zbl0373.14007MR485870
27. [27] J. Steenbrink: Cohomologically insignificant degenerations. Compositio Math.42 (1981) 315-320. Zbl0428.32017MR607373
28. [28] G. Tjurina: On a type of contractible curves. Doklady Akad. Nauk SSSR, 1973 (1967), 529-531 (Soviet Math. Doklady, 8(196), 441-443). Zbl0176.50803MR215849
29. [29] PH. Wagreich: Elliptic singularities of surfaces. Amer. J. Math., 92 (1970), 419-454. Zbl0204.54501MR291170

1. J. H. M. Steenbrink, Cohomologically insignificant degenerations
2. Jonathan M. Wahl, A characterization of quasi-homogeneous Gorenstein surface singularities