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[A]Atiyah, M. F., The logarithm of the Dedekind eta function.Math. Ann., 278 (1987), 335–380.
[APS1]Atiyah, M. F., Patodi, V. K. &Singer, I. M., Spectral asymmetry and Riemannian geometry. I.Math. Proc. Cambridge Philos. Soc., 77 (1975), 43–69.
[APS1] —, Spectral asymmetry and Riemannian geometry IIMath. Proc. Cambridge Philos. Soc., 79 (1976), 71–99.
[B]Bismut, J.-M., Demailly's asymptotic Morse inequalities: a heat equation proof.J. Funct. Anal., 72 (1987), 263–278.
[Ba]Barlet, D., Développement asymptotique des fonctions obtenues par intégration dans la fibre.Invent. math., 68 (1982), 129–174.
[BB]Bismut, J.-M. &Bost, J.-B., Fibrés déterminants, métriques de Quillen et dégénérescence des courbes.C. R. Acad. Sci. Paris Sér I, 307 (1988), 317–320.
[BC]Bott, R. &Chern, S.-S., Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections.Acta Math., 114 (1968), 71–112.
[BF]Bismut, J. M. &Freed, D. S., The analysis of elliptic families I, II.Comm. Math. Phys., 106 (1986), 159–176 and 107 (1986), 103–163.
[BGS1]Bismut, J. M., Gillet, H. &Soulé, C., Analytic torsion and holomorphic determinant bundles. I. Bout-Chern forms and analytic torsion.Comm. Math. Phys., 115 (1988), 49–78.
[BGS2] —, Analytic torsion and holomorphic determinant bundles. II. Direct images and Bott-Chern forms.Comm. Math. Phys., 115 (1988), 79–126.
[BGS3] —, Analytic torsion and holomorphic determinant bundles. III. Quillen metrics and holomorphic determinants.Comm. Math. Phys., 115 (1988), 301–351.
[BK]Belavin, A. & Knizhnik, V., Complex geometry and theory of quantum strings. Landau Institute Preprint.
[BS]Borel, A. &Serre, J.-P., Le théorème de Riemann-Roch, d'après Grothendieck.Bull. Soc. Math. France, 86 (1958), 97–136.
[Ch]Chern, S.-S.,Complex Manifolds without Potential Theory. 2nd edition. Springer Verlag, 1979.
[CGT]Cheeger, J., Gromov, M. &Taylor, M., Finite propagation speed, kernel estimates for functions of the Laplace operator and the geometry of Riemannian complete manifolds.J. Differential Geom., 17 (1982), 15–53.
[D]Deligne, P., Le déterminant de la cohomologie.Contemporary Mathematics, Vol. 67, 93–178.
[DM]Deligne, P. &Mumford, D., The irreducibility of the space of curves of a given genus.Inst. Hautes Études Sci. Publ. Math., 36 (1969), 75–109.
[F]Faltings, G., Endlichkeitssätze für abelsche Varietäten über Zahlkörpern,Invent. Math., 73 (1983), 349–366.
[GR]Grauert, H. &Remmert, R., Bilder und Urbilder analytischer Garben.Ann. of Math., 68 (1958), 393–443.
[Grau]Grauert, H., Über Modifikationen und exzeptionelle analytische Mengen.Math. Ann., 146 (1962), 331–368.
[Gro]Grothendieck, A., Techniques de construction en géométrie analytique. VIII. Rapport sur les théorèmes de finitude de Grauert et Remmert.Seminaire H. Cartan, 1960–61.
[I]Igusa, J.-I., Complex powers and asymptotic expansions. I. Functions of certain types.J. Reine Angew. Math., 268/269, (1974), 110–130; II. Asymptotic expansions.J. Reine Angew. Math., 278/279, (1975), 307–321.
[IMK]Itô, K. &McKean, H.,Diffusion Process and their Sample Paths. Grundl. Math. Wiss. Band 125. Berlin-Heidelberg-New York, Springer, 1974.
[K]Knudsen, F. F., The projectivity of the moduli space of stable curves II: The stacksM g,n. III: The line bundles onM g,n and a proof of the projectivity ofM g,n in characteristic 0.Math. Scand., 52 (1983), 161–199, 200–212.
[KM]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.
[KV]Kiehl, R. &Verdier, J.-L., Ein einfacher Beweis des Kohärenzsatzes von Grauert.Math. Ann., 195 (1971), 24–50.
[M]Mumford, D., Stability of projective varieties.Enseign. Math., 23 (1977), 39–110.
[MKS]McKean, H. &Singer, I. M., Curvature and the eigenvalues of the Laplacian.J. Differential Geom., 1 (1967), 43–69.
[R]Raynaud, M. (Mme), Géométrie algébrique et géométrie analytique. Exposé XII.Séminaire de géométrie algébrique du Bois Marie, 1960/61, dirigé par A. Grothendieck.Springer Lecture Notes in Mathematics, 224 (1971), 311–343.
[Rau]Rauch, H. E., The singularities of the modulus space.Bull. Amer. Math. Soc., 68 (1962), 390–394.
[S]Serre, J. P.,Cours d'arithmétique. Paris, Presses Universitaires de France, 1970.
[Sz]Szpiro, L.,Séminaire sur les pinceaux arithmétiques: la conjecture de Mordell. Astérisque, 127 (1985).
[T]Tjurina, G. N., Locally seminniversal flat deformations of singularities of complex spaces.Math. USSR-Izv., 3 (1970), 967–998.
[W]Weil, A.,Elliptic Functions according to Eisenstein and Kronecker. Springe-Verlag, 1976.
[Wi]Witten, E., Global gravitational anomalies.Comm. Math. Phys., 100 (1985), 197–229.
[Wo]Wolpert, S., Asymptotics of the spectrum and the Selberg zeta function of Riemann surfaces.Comm. Math. Phys., 112 (1987), 283–315.
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Bismut, J.M., Bost, J.B. Fibrés déterminants, métriques de Quillen et dégénérescence des courbes. Acta Math. 165, 1–103 (1990). https://doi.org/10.1007/BF02391902
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DOI: https://doi.org/10.1007/BF02391902