References
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.
Arakelov S., Intersection theory of divisors on an arithmetic surface,Izv. Akad. Nauk SSSR., Ser. Mat., 38 (1974), no 6.AMS Translation, 8 (1974), no 6, 1167–1180.
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.
Atiyah M. F., Bott R., Patodi V. K., On the heat equation and the Index Theorem,Invent. Math., 19 (1973), 279–330.
Atiyah M. F., Singer I. M., The index of elliptic operators, III,Ann. of Math., 87 (1968), 546–604.
Baum P., Fulton W., MacPherson R., Riemann-Roch for singular varieties,Publ. Math. IHES, 45 (1975), 101–146.
Berline N., Vergne M., A proof of Bismut local index theorem for a family of Dirac operators,Topology, 26 (1987), 435–463.
Bismut J. M., The index Theorem for families of Dirac operators: two heat equation proofs,Invent. Math., 83 (1986), 91–151.
Bismut J. M., Superconnection currents and complex immersions,Invent. Math., 99 (1990), 59–113.
Bismut J. M., Koszul complexes, harmonic oscillators and the Todd class,J.A.M.S., 3 (1990), 159–256.
Bismut J. M.,Large deviations and the Malliavin calculus, Prog. Math. no 45, Basel-Boston-Stuttgart, Birkhäuser, 1984.
Bismut J. M., The Atiyah-Singer Index Theorems: a probabilistic approach, I,J. Funct. Anal., 57 (1984), 56–99.
Bismut J. M., Demailly’s asymptotic Morse inequalities: a heat equation proof,J. Funct. Anal., 72 (1987), 263–278.
Bismut J. M., The Witten complex and the degenerate Morse inequalities,J. of Diff. Geom., 23 (1986), 207–240.
Bismut J. M., Gillet H., Soulé C., Analytic torsion and holomorphic determinant bundles, I,Comm. Math. Phys., 115 (1988), 49–78.
Bismut J. M., Gillet H., Soulé C., Analytic torsion and holomorphic determinant bundles, II,Comm. Math. Phys., 115 (1988), 79–126.
Bismut J. M., Gillet H., Soulé C., Analytic torsion and holomorphic determinant bundles, III,Comm. Math. Phys., 115 (1988), 301–351.
Bismut J. M., Gillet H., Soulé C., Bott-Chern currents and complex immersions.Duke Math. Journal, 60 (1990), 255–284.
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. no 86, Boston-Basel-Berlin, Birkhaüser, 1990.
Bismut J. M., Lebeau G., Immersions complexes et métriques de Quillen.C.R. Acad. Sci. Paris, 309, Série I (1989), 487–491.
Bott R., Chern S. S., Hermitian vector bundles and the equidistribution of the zeros of their holomorphic sections,Acta Math., 114 (1968), 71–112.
Chazarain J., Piriou A.,Introduction à la théorie des équations aux dérivées partielles linéaires, Paris, Gauthier-Villars, 1981.
Cheeger J., Analytic torsion and the heat equation,Ann. of Math., 109 (1979), 259–322.
Deligne P., Le déterminant de la cohomologie,Contemporary mathematics, 67 (1987), 93–177.
Donaldson S., Anti-self dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles,Proc. London Math. Soc., 50 (1985), 1–26.
Dynkin E. B., Diffusion of tensors,Soviet Math Doklady, 9 (1968), 532–535.
Eilenberg S., Homological dimension and local syzygies,Ann. of Math., 64 (1956), 328–336.
Faltings G., Calculus on arithmetic surfaces,Ann. of Math., 119 (1984), 387–424.
Getzler E, A short proof of the Atiyah-Singer Index Theorem,Topology, 25 (1986), 111–117.
Gillet H., Soulé C., Arithmetic Intersection Theory,Publ. Math. IHES, 72 (1990), 93–174.
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.
Gillet H., Soulé C., Analytic torsion and the arithmetic Todd genus.Topology, 30 (1991), 21–54.
Gillet H., Soulé C., Un théorème de Rieman-Roch-Grothendieck arithmétique.C.R. Acad. Sci. Paris, 309, Série I (1989), 929–932.
Glimm J., Jaffe A.,Quantum physics, Berlin, Heidelberg, New York, Springer, 1987.
Griffiths P., Harris J.,Principles of algebraic geometry, New York, Wiley, 1978.
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.
Helffer B., Sjöstrand J., Puits multiples en limite semi-classique. VI, Cas des puits sous-variétés,Ann. Inst. H. Poincaré, 46 (1987), 353–372.
Helffer B., Sjöstrand J., A proof of the Bott inequalities, inAlgebraic Analysis, Vol. I, M. Kashiwara, T. Kawai ed., New York, Academic Press, 1988, 171–183.
Hirzebruch F., Arithmetic genera and the theorem of Riemann-Roch for algebraic varieties.Proc. Natl. Acad. Sci., USA, 40 (1954), 110–114.
Hitchin N. J., Harmonic spinors.Adv. in Math., 14 (1974), 1–55.
Itô K., Stochastic parallel displacement, inProbabilistic methods in differential equations, Lecture Notes in Mathematics no 45, Berlin, Heidelberg, New York, Springer, 1975, 1–7.
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.
Kobayashi S.,Differential geometry of complex vector bundles, Iwanami Shoten and Princeton University Press, 1987.
Kobayashi S., Nomizu K.,Foundations of differential geometry, II, New York, Interscience, 1969.
Lang S.,Introduction to Arakelov theory, Berlin, Heidelberg, New York, Springer, 1988.
Lichnerowicz A., Spineurs harmoniques,C.R. Acad. Sci. Paris, Série A, 257 (1963), 7–9.
McKean H., Singer I. M., Curvature and the eigenvalues of the Laplacian,J. of Diff. Geom., 1 (1967), 43–69.
Müller W., Analytic torsion and R. torsion of Riemannian manifolds,Adv. in Math., 28 (1978), 233–305.
Quillen D., Superconnections and the Chern character,Topology, 24 (1985), 89–95.
Quillen D., Determinants of Cauchy-Riemann operators over a Riemann surface,Funct. Anal. Appl., 14 (1985), 31–34.
Ray D. B., Singer I. M., R.torsion and the Laplacian on Riemannian manifolds,Adv. in Math., 7 (1971), 145–210.
Ray D. B., Singer I. M., Analytic torsion for complex manifolds,Ann. of Math., 98 (1973), 154–177.
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.
Seeley R. T., Complex powers of an elliptic operator.Proc. Symp. Pure and Appl. Math. AMS, 10 (1967), 288–307.
Serre J. P.,Algèbre locale. Multiplicités. Lecture Notes in Math. no 11, Berlin, Heidelberg, New York, Springer, 1965.
Tangerman F. M., To appear.
Taylor M.,Pseudodifferential operators, Princeton, Princeton Univ. Press, 1981.
Witten E., Supersymmetry and Morse theory,J. Differential Geom., 17 (1982), 661–692.
Author information
Authors and Affiliations
About this article
Cite this article
Bismut, JM., Lebeau, G. Complex immersions and Quillen metrics. Publications Mathématiques de l’Institut des Hautes Scientifiques 74, 1–291 (1991). https://doi.org/10.1007/BF02699352
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02699352