Holomorphic families of immersions and higher analytic torsion forms
Astérisque, no. 244 (1997), 283 p.
@book{AST_1997__244__R1_0,
     author = {Bismut, Jean-Michel},
     title = {Holomorphic families of immersions and higher analytic torsion forms},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {244},
     year = {1997},
     zbl = {0899.32013},
     mrnumber = {1623496},
     language = {en},
     url = {http://www.numdam.org/item/AST_1997__244__R1_0}
}
Bismut, Jean-Michel. Holomorphic families of immersions and higher analytic torsion forms. Astérisque, no. 244 (1997), 283 p. http://www.numdam.org/item/AST_1997__244__R1_0/

[1] Atiyah M. F., Bott R., Patodi V. K., On the heat equation and the Index Theorem, Invent Math., 19 (1973), 279-330. | Article | MR 650828 | Zbl 0257.58008

[2] Baum P., Fulton W., Macpherson R., Riemann-Roch for singular varieties, Publ. Math. IHES, 45 (1975), 101-146. | Article | Numdam | MR 412190 | Zbl 0332.14003

[3] Berline N., Getzler E., Vergne M., Heat kernels and Dirac operators, Grundl. Math. Wiss. Band 298. Berlin-Heidelberg-New-York, Springer 1992. | MR 1215720 | Zbl 0744.58001

[4] Bismut J.-M., The index Theorem for families of Dirac operators: two heat equation proofs, Invent. Math., 83 (1986), 91-151. | Article | MR 813584 | Zbl 0592.58047

[5] Bismut J.-M., Superconnection currents and complex immersions, Invent. Math., 99 (1990), 59-113. | Article | MR 1029391 | Zbl 0696.58006

[6] Bismut J.-M., Koszul complexes, harmonic oscillators and the Todd class, J.A.M.S., 3 (1990), 159-256. | MR 1017783 | Zbl 0702.58071

[7] Bismut J.-M., Formules de Lichnerowicz et théorème de l'indice, Proceedings of the Conference in honour of A. Lichnerowicz, D. Bernard, Y. Choquet-Bruhat eds., Vol. Géom. Diff. pp 11-31. Travaux en cours, Paris: Hermann 1988. | MR 955849 | Zbl 0648.58033

[8] Bismut J.-M., Equivariant short exact sequences of vector bundles and their analytic torsion forms. Comp. Math., 93 (1994), 291-354. | Numdam | MR 1300765 | Zbl 0817.32014

[9] Bismut J.-M., The infinitesimal Lefschetz formulas: a heat equation proof, J. Fund. Anal., 62 (1985), 435-457. | Article | MR 794778 | Zbl 0572.58021

[10] Bismut J.-M., Familles d'immersions et formes de torsion analytique en degré supérieur. C.R. Acad. Sci. Paris, 320, série I (1995), 969-974. | MR 1328720 | Zbl 0844.32010

[11] Bismut J.-M., Berthomieu A., Quillen metrics and higher analytic torsion forms, J. reine angew. Math., 457 (1994), 85-184 | MR 1305280 | Zbl 0804.32017

[12] Bismut J.-M., Cheeger J., η-invariants and their adiabatic limits, J.A.M.S., 2 (1989), 33-70. | MR 966608 | Zbl 0671.58037

[13] Bismut J.-M., Gillet H., Soulé C., Analytic torsion and holomorphic determinants bundles, I, Comm. Math. Phys., 115 (1988), 49-78. | Article | MR 929146 | Zbl 0651.32017

[14] Bismut J.-M., Gillet H., Soulé C., Analytic torsion and holomorphic determinants bundles, II, Comm. Math. Phys., 115 (1988), 79-126. | Article | Zbl 0651.32017

[15] Bismut J.-M., Gillet H., Soulé C., Analytic torsion and holomorphic determinants bundles, III, Comm. Math. Phys., 115 (1988), 301-351. | Article | MR 931666 | Zbl 0651.32017

[16] Bismut J.-M., Gillet H., Soulé C., Bott-Chern currents and complex immersions. Duke Math. Journal, 60 (1990), 255-284. | Article | MR 1047123 | Zbl 0697.58005

[17] Bismut J.-M., Gillet H., Soulé C., Complex immersions and Arakelov geometry, The Grothendieck Festschrift, P. Cartier and al. eds, pp. 249-331. Prog. Math. n° 86. Boston-Basel-Berlin, Birkhäuser, 1990. | MR 1086887 | Zbl 0744.14015

[18] Bismut J.-M., Köhler K., Higher analytic torsion forms and anomaly formulas, J. of Alg. Geom., 1 (1992), 647-684. | MR 1174905 | Zbl 0784.32023

[19] Bismut J.-M., Lebeau G., Complex immersions and Quillen metrics, Publ. Math. IHES, 74 (1991), 1-297. | Article | Numdam | MR 1188532 | Zbl 0784.32010

[20] Bott R., Chern S. S., Hermitian vector bundles and the equidistribution of the zeros of their holomorphic sections, Acta Math., 114 (1968), 71-112. | Article | MR 185607 | Zbl 0148.31906

[21] Chazarain J., Piriou A., Introduction à la théorie des équations aux dérivées partielles linéaires, Paris, Gauthier-Villars, 1981. | MR 598467 | Zbl 0446.35001

[22] Faltings G., Lectures on the arithmetic Riemann-Roch theorem, Ann. Math. Studies, Princeton University Press, Princeton 1992 | MR 1158661 | Zbl 0744.14016

[23] Getzler E., A short proof of the Atiyah-Singer Index Theorem, Topology, 25 (1986), 111-117. | Article | MR 836727 | Zbl 0607.58040

[24] Gillet H., Soulé C., Arithmetic Intersection Theory, Publ. Math. IHES, 72 (1990), 93-174. | Article | Numdam | MR 1087394 | Zbl 0741.14012

[25] Gillet H., Soulé C., Characteristic classes of algebraic vector bundles with Hermitian metric, Ann. of Math., I, 131 (1990), 163-203. | Article | MR 1038362 | Zbl 0715.14018

Gillet H., Soulé C., Characteristic classes of algebraic vector bundles with Hermitian metric, Ann. of Math., II, 131 (1990), 205-238. | Article | MR 1043268 | Zbl 0715.14006

[26] Gillet H., Soulé C., Analytic torsion and the arithmetic Todd genus, Topology, 30 (1991), 21-54. | Article | MR 1081932 | Zbl 0787.14005

[27] Gillet H., Soulé C., An arithmetic Riemann-Roch Theorem, Invent. Math., 110 (1992), 473-543. | Article | MR 1189489 | Zbl 0777.14008

[28] Griffiths P., Harris J., Principles of algebraic geometry, New-York, Wiley, 1978. | MR 507725 | Zbl 0836.14001 | Zbl 0408.14001

[29] Hitchin N., Harmonic spinors, Adv. Math., 14 (1974), 1-55 | Article | MR 358873 | Zbl 0284.58016

[30] Hörmander L., The analysis of linear partial differential operators, I, Grundl. Math. Wiss. Band 256, Berlin-Heidelberg-New-York, Springer, 1983. | MR 717035 | Zbl 0521.35001

[31] Kobayashi S., Differential geometry of complex vector bundles. Iwanami Shoten and Princeton University Press, 1987. | Article | MR 909698 | Zbl 0708.53002

[32] Quillen D., Superconnections and the Chern character, Topology, 24 (1985), 89-95. | Article | MR 790678 | Zbl 0569.58030

[33] Quillen D., Determinants of Cauchy-Riemann operators over a Riemann surface, Funct. Anal. Appl., 14 (1985), 31-34. | Article | Zbl 0603.32016

[34] Ray D. B., Singer I., Analytic torsion for complex manifolds, Ann. of Math., 98 (1973), 154-177. | Article | MR 383463 | Zbl 0267.32014

[35] Taylor M., Pseudodifferential operators, Princeton, Princeton Univ. Paris, 1981. | MR 618463 | Zbl 0453.47026