Complex immersions and Quillen metrics

 Access to full text

 Full (PDF)

1. [AlGBMNV] ALVAREZ-GAUMÉ L., BOST J. B., MOORE G., NELSON P., VAFA C., Bosonization on higher genus Riemann surfaces, Comm. Math. Phys., 112 (1987), 503-552. Zbl0647.14019MR88j:81061
2. [Ar] ARAKELOV S., Intersection theory of divisors on an arithmetic surface, Izv. Akad. Nauk SSSR., Ser. Mat., 38 (1974), n° 6. AMS Translation, 8 (1974), n° 6, 1167-1180. Zbl0355.14002MR57 #12505
3. [ABo] ATIYAH M. F., BOTT R, A Lefschetz fixed point formula for elliptic complexes, I, Ann. Math., 86 (1967), 374-407 ; II, Ann. of Math., 88 (1968), 451-491. Zbl0161.43201MR35 #3701
4. [ABoP] ATIYAH M. F., BOTT R., PATODI V. K., On the heat equation and the Index Theorem, Invent. Math., 19 (1973), 279-330. Zbl0257.58008MR58 #31287
5. [AS] ATIYAH M. F., SINGER I. M., The index of elliptic operators, III, Ann. of Math., 87 (1968), 546-604. Zbl0164.24301MR38 #5245
6. [BaFM] BAUM P., FULTON W., MACPHERSON R., Riemann-Roch for singular varieties, Publ. Math. IHES, 45 (1975), 101-146. Zbl0332.14003MR54 #317
7. [BeV] BERLINE N., VERGNE M., A proof of Bismut local index theorem for a family of Dirac operators, Topology, 26 (1987), 435-463. Zbl0636.58030MR88m:58179
8. [B1] BISMUT J. M., The index Theorem for families of Dirac operators : two heat equation proofs, Invent. Math., 83 (1986), 91-151. Zbl0592.58047MR87g:58117
9. [B2] BISMUT J. M., Superconnection currents and complex immersions, Invent. Math., 99 (1990), 59-113. Zbl0696.58006MR91b:58240
10. [B3] BISMUT J. M., Koszul complexes, harmonic oscillators and the Todd class, J.A.M.S., 3 (1990), 159-256. Zbl0702.58071MR91b:58245
11. [B4] BISMUT J. M., Large deviations and the Malliavin calculus, Prog. Math. n° 45, Basel-Boston-Stuttgart, Birkhäuser, 1984. Zbl0537.35003MR86f:58150
12. [B5] BISMUT J. M., The Atiyah-Singer Index Theorems : a probabilistic approach, I, J. Funct. Anal., 57 (1984), 56-99. Zbl0538.58033MR86g:58128a
13. [B6] BISMUT J. M., Demailly's asymptotic Morse inequalities : a heat equation proof, J. Funct. Anal., 72 (1987), 263-278. Zbl0649.58030MR88j:58131
14. [B7] BISMUT J. M., The Witten complex and the degenerate Morse inequalities, J. of Diff. Geom., 23 (1986), 207-240. Zbl0608.58038MR87m:58169
15. [BGS1] BISMUT J. M., GILLET H., SOULÉ C., Analytic torsion and holomorphic determinant bundles, I, Comm. Math. Phys., 115 (1988), 49-78. Zbl0651.32017MR89g:58192a
16. [BGS2] BISMUT J. M., GILLET H., SOULÉ C., Analytic torsion and holomorphic determinant bundles, II, Comm. Math. Phys., 115 (1988), 79-126. Zbl0651.32017MR89g:58192b
17. [BGS3] BISMUT J. M., GILLET H., SOULÉ C., Analytic torsion and holomorphic determinant bundles, III, Comm. Math. Phys., 115 (1988), 301-351. Zbl0651.32017MR89g:58192c
18. [BGS4] BISMUT J. M., GILLET H., SOULÉ C., Bott-Chern currents and complex immersions. Duke Math. Journal, 60 (1990), 255-284. Zbl0697.58005MR91d:58239
19. [BGS5] BISMUT J. M., GILLET H., SOULÉ C., Complex immersions and Arakelov geometry, The Grothendieck Festschrift, P. Cartier and al. ed., pp. 249-331. Prog. Math. n° 86, Boston-Basel-Berlin, Birkhaüser, 1990. Zbl0744.14015MR92a:14019
20. [BL] BISMUT J. M., LEBEAU G., Immersions complexes et métriques de Quillen. C.R. Acad. Sci. Paris, 309, Série I (1989), 487-491. Zbl0681.53034MR91k:58138
21. [BoC] BOTT R., CHERN S. S., Hermitian vector bundles and the equidistribution of the zeros of their holomorphic sections, Acta Math., 114 (1968), 71-112. Zbl0148.31906MR32 #3070
22. [CP] CHAZARAIN J., PIRIOU A., Introduction à la théorie des équations aux dérivées partielles linéaires, Paris, Gauthier-Villars, 1981. Zbl0446.35001MR82i:35001
23. [Ch] CHEEGER J., Analytic torsion and the heat equation, Ann. of Math., 109 (1979), 259-322. Zbl0412.58026MR80j:58065a
24. [De] DELIGNE P., Le déterminant de la cohomologie, Contemporary mathematics, 67 (1987), 93-177. Zbl0629.14008MR89b:32038
25. [Do] DONALDSON S., Anti-self dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc., 50 (1985), 1-26. Zbl0529.53018MR86h:58038
26. [Dy] DYNKIN E. B., Diffusion of tensors, Soviet Math Doklady, 9 (1968), 532-535. Zbl0188.27002MR38 #2840
27. [E] EILENBERG S., Homological dimension and local syzygies, Ann. of Math., 64 (1956), 328-336. Zbl0073.26003MR18,558c
28. [F] FALTINGS G., Calculus on arithmetic surfaces, Ann. of Math., 119 (1984), 387-424. Zbl0559.14005MR86e:14009
29. [Ge] GETZLER E, A short proof of the Atiyah-Singer Index Theorem, Topology, 25 (1986), 111-117. Zbl0607.58040MR87h:58207
30. [GS1] GILLET H., SOULÉ C., Arithmetic Intersection Theory, Publ. Math. IHES, 72 (1990), 93-174. Zbl0741.14012MR92d:14016
31. [GS2] GILLET H., SOULÉ C., Characteristic classes for algebraic vector bundles with Hermitian metric, Ann. of Math., I, 131 (1990), 163-203, II, 131 (1990), 205-238. Zbl0715.14018MR91m:14032a
32. [GS3] GILLET H., SOULÉ C., Analytic torsion and the arithmetic Todd genus. Topology, 30 (1991), 21-54. Zbl0787.14005MR92d:14015
33. [GS4] GILLET H., SOULÉ C., Un théorème de Rieman-Roch-Grothendieck arithmétique. C.R. Acad. Sci. Paris, 309, Série I (1989), 929-932. Zbl0732.14002MR91m:14031
34. [GlJ] GLIMM J., JAFFE A., Quantum physics, Berlin, Heidelberg, New York, Springer, 1987. Zbl0461.46051MR89k:81001
35. [GrH] GRIFFITHS P., HARRIS J., Principles of algebraic geometry, New York, Wiley, 1978. Zbl0408.14001MR80b:14001
36. [HeSj1] HELFFER B., SJÖSTRAND J., Puits multiples en limite semi-classique. IV, Étude du complexe de Witten, Comm. in P.D.E., 10 (1985), 245-340. Zbl0597.35024
37. [HeSj2] HELFFER B., SJÖSTRAND J., Puits multiples en limite semi-classique. VI, Cas des puits sous-variétés, Ann. Inst. H. Poincaré, 46 (1987), 353-372. Zbl0648.35027
38. [HeSj3] HELFFER B., SJÖSTRAND J., A proof of the Bott inequalities, in Algebraic Analysis, Vol. I, M. Kashiwara, T. Kawai ed., New York, Academic Press, 1988, 171-183. Zbl0693.58019MR90g:58018
39. [H] HIRZEBRUCH F., Arithmetic genera and the theorem of Riemann-Roch for algebraic varieties. Proc. Natl. Acad. Sci., USA, 40 (1954), 110-114. Zbl0055.38803MR17,535a
40. [Hi] HITCHIN N. J., Harmonic spinors. Adv. in Math., 14 (1974), 1-55. Zbl0284.58016MR50 #11332
41. [I] ITÔ K., Stochastic parallel displacement, in Probabilistic methods in differential equations, Lecture Notes in Mathematics n° 45, Berlin, Heidelberg, New York, Springer, 1975, 1-7. Zbl0308.60027MR52 #15704
42. [KnM] KNUDSEN F. F., MUMFORD D., The projectivity of the moduli space of stable curves, I, Preliminaries on "det" and "div", Math. Scand., 39 (1976), 19-55. Zbl0343.14008MR55 #10465
43. [K] KOBAYASHI S., Differential geometry of complex vector bundles, Iwanami Shoten and Princeton University Press, 1987. Zbl0708.53002MR89e:53100
44. [KN] KOBAYASHI S., NOMIZU K., Foundations of differential geometry, II, New York, Interscience, 1969. Zbl0175.48504MR38 #6501
45. [La] LANG S., Introduction to Arakelov theory, Berlin, Heidelberg, New York, Springer, 1988. Zbl0667.14001MR89m:11059
46. [Li] LICHNEROWICZ A., Spineurs harmoniques, C.R. Acad. Sci. Paris, Série A, 257 (1963), 7-9. Zbl0136.18401MR27 #6218
47. [MKS] MCKEAN H., SINGER I. M., Curvature and the eigenvalues of the Laplacian, J. of Diff. Geom., 1 (1967), 43-69. Zbl0198.44301MR36 #828
48. [Mü] MÜLLER W., Analytic torsion and R. torsion of Riemannian manifolds, Adv. in Math., 28 (1978), 233-305. Zbl0395.57011MR80j:58065b
49. [Q1] QUILLEN D., Superconnections and the Chern character, Topology, 24 (1985), 89-95. Zbl0569.58030MR86m:58010
50. [Q2] QUILLEN D., Determinants of Cauchy-Riemann operators over a Riemann surface, Funct. Anal. Appl., 14 (1985), 31-34. Zbl0603.32016MR86g:32035
51. [RS1] RAY D. B., SINGER I. M., R.torsion and the Laplacian on Riemannian manifolds, Adv. in Math., 7 (1971), 145-210. Zbl0239.58014MR45 #4447
52. [RS2] RAY D. B., SINGER I. M., Analytic torsion for complex manifolds, Ann. of Math., 98 (1973), 154-177. Zbl0267.32014MR52 #4344
53. [ReSi] REED M., SIMON B., Methods of modern mathematical physics, Vol. I, Functional Analysis, New York, Academic Press, 1972. Vol. II, Fourier analysis, self-adjointness, New York, Academic Press, 1975. Zbl0242.46001
54. [Se] SEELEY R. T., Complex powers of an elliptic operator. Proc. Symp. Pure and Appl. Math. AMS, 10 (1967), 288-307. Zbl0159.15504MR38 #6220
55. [Ser] SERRE J. P., Algèbre locale. Multiplicités. Lecture Notes in Math. n° 11, Berlin, Heidelberg, New York, Springer, 1965. Zbl0142.28603MR34 #1352
56. [Ta] TANGERMAN F. M., To appear. 
57. [T] TAYLOR M., Pseudodifferential operators, Princeton, Princeton Univ. Press, 1981. Zbl0453.47026MR82i:35172
58. [W] WITTEN E., Supersymmetry and Morse theory, J. Differential Geom., 17 (1982), 661-692. Zbl0499.53056MR84b:58111

1. Ursula Ludwig, The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions
2. Jean-Michel Bismut, Le Laplacien hypoelliptique
3. Jean-Michel Bismut, Equivariant short exact sequences of vector bundles and their analytic torsion forms
4. Ursula Ludwig, A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation
5. Xiaonan Ma, Flat vector bundles and analytic torsion forms
6. Christophe Soulé, Genres de Todd et valeurs aux entiers des dérivées de fonctions $L$
7. Ma Xiaonan, Formes de torsion analytique et familles des submersions I
8. Werner Müller, Relative determinants of elliptic operators and scattering theory
9. Xiaonan Ma, Submersions and equivariant Quillen metrics
10. Ahmed Abbes, Thierry Bouche, Théorème de Hilbert-Samuel «arithmétique»