Analytic torsion for line bundles on Riemann surfaces



Duke Mathematical Journal

Analytic torsion for line bundles on Riemann surfaces

Jay Jorgenson

Source: Duke Math. J. Volume 62, Number 3 (1991), 527-549.

First Page PDF: View first page of article (PDF, 113 KB)

Primary Subjects: 58G26
Secondary Subjects: 14G40, 14H55

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Alternatively, the document is available for a cost of $25. Select the "buy article" button below to purchase this document from a secured VeriSign, Inc. site.
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077296504
Mathematical Reviews number (MathSciNet): MR1104806
Zentralblatt MATH identifier: 0749.57005
Digital Object Identifier: doi:10.1215/S0012-7094-91-06222-8

References

[A1] L. Alvarez-Gaume, J.-B. Bost, G. Moore, P. Nelson, and C. Vafa, Bosonization on higher genus Riemann surfaces, Comm. Math. Phys. 112 (1987), no. 3, 503–552.
Mathematical Reviews (MathSciNet): MR88j:81061
Zentralblatt MATH: 0647.14019
Digital Object Identifier: doi:10.1007/BF01218489
[A2] L. Alvarez-Gaumé, G. Moore, P. Nelson, C. Vafa, and J.-B. Bost, Bosonization in arbitrary genus, Phys. Lett. B 178 (1986), no. 1, 41–47.
Mathematical Reviews (MathSciNet): MR87m:81146
Digital Object Identifier: doi:10.1016/0370-2693(86)90466-1
[A-M-V] L. Alvarez-Gaumé, G. Moore, P. Nelson, C. Vafa, and J.-B. Bost, Theta functions, modular invariance, and strings, Comm. Math. Phys. 106 (1986), no. 1, 1–40.
Mathematical Reviews (MathSciNet): MR88e:32030
Zentralblatt MATH: 0605.58049
Digital Object Identifier: doi:10.1007/BF01210925
[B] J.-B. Bost, Conformal and holomorphic anomalies on Riemann surfaces and determinant line bundles, VIIIth international congress on mathematical physics (Marseille, 1986), World Sci. Publishing, Singapore, 1987, pp. 768–775.
Mathematical Reviews (MathSciNet): MR89h:58178
[Fa] G. Faltings, Calculus on arithmetic surfaces, Ann. of Math. (2) 119 (1984), no. 2, 387–424.
Mathematical Reviews (MathSciNet): MR86e:14009
Zentralblatt MATH: 0559.14005
Digital Object Identifier: doi:10.2307/2007043
[F-K] H. Farkas and I. Kra, Riemann surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York, 1980.
Mathematical Reviews (MathSciNet): MR82c:30067
Zentralblatt MATH: 0475.30001
[F1] J. Fay, Analytic torsion and Prym differentials, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 107–122.
Mathematical Reviews (MathSciNet): MR83a:14034
Zentralblatt MATH: 0458.30025
[F2] J. Fay, Theta functions on Riemann surfaces, Lecture Notes in Mathematics, vol. 352, Springer-Verlag, Berlin, 1973.
Mathematical Reviews (MathSciNet): MR49:569
Zentralblatt MATH: 0281.30013
[F3] J. D. Fay, Perturbation of analytic torsion on Riemann Surfaces, preprint, 1989.
[Fo] O. Forster, Lectures on Riemann surfaces, Graduate Texts in Mathematics, vol. 81, Springer-Verlag, New York, 1981.
Mathematical Reviews (MathSciNet): MR83d:30046
Zentralblatt MATH: 0475.30002
[G-H] P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley-Interscience [John Wiley & Sons], New York, 1978.
Mathematical Reviews (MathSciNet): MR80b:14001
Zentralblatt MATH: 0408.14001
[Gu] R. C. Gunning, Lectures on Riemann surfaces, Princeton Mathematical Notes, Princeton University Press, Princeton, N.J., 1966.
Mathematical Reviews (MathSciNet): MR34:7789
Zentralblatt MATH: 0175.36801
[He1] D. A. Hejhal, Theta functions, kernel functions, and Abelian integrals, vol. 129, Memoirs AMS, Providence, R.I., 1972.
Mathematical Reviews (MathSciNet): MR51:8403
Zentralblatt MATH: 0244.30016
[He2] D. A. Hejhal, The Selberg trace formula for ${\rm PSL}(2,\,{\bf R})$. Vol. 2, Lecture Notes in Mathematics, vol. 1001, Springer-Verlag, Berlin, 1983.
Mathematical Reviews (MathSciNet): MR86e:11040
Zentralblatt MATH: 0543.10020
[J1] J. Jorgenson, Asymptotic behavior of Faltings's delta function, Duke Math. J. 61 (1990), no. 1, 221–254.
Mathematical Reviews (MathSciNet): MR91m:14042
Zentralblatt MATH: 0746.30032
Digital Object Identifier: doi:10.1215/S0012-7094-90-06111-3
Project Euclid: euclid.dmj/1077296655
[J2] J. Jorgenson, Faltings's delta function and analytic torsion for line bundles, Ph.D. thesis, Stanford University, 1989.
[Ka] T. Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966.
Mathematical Reviews (MathSciNet): MR34:3324
Zentralblatt MATH: 0148.12601
[Ko] K. Kodaira, Complex manifolds and deformation of complex structures, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 283, Springer-Verlag, New York, 1986.
Mathematical Reviews (MathSciNet): MR87d:32040
Zentralblatt MATH: 0581.32012
[K] S. G. Krantz, Function theory of several complex variables, John Wiley & Sons Inc., New York, 1982.
Mathematical Reviews (MathSciNet): MR84c:32001
Zentralblatt MATH: 0471.32008
[La] S. Lang, Introduction to algebraic and abelian functions, Graduate Texts in Mathematics, vol. 89, Springer-Verlag, New York, 1982.
Mathematical Reviews (MathSciNet): MR84m:14032
Zentralblatt MATH: 0513.14024
[M-P] S. Minakshisundaram and Ȧ. Pleijel, Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds, Canadian J. Math. 1 (1949), 242–256.
Mathematical Reviews (MathSciNet): MR11,108b
Zentralblatt MATH: 0041.42701
[Mu1] D. Mumford, Tata lectures on theta. I, Progress in Mathematics, vol. 28, Birkhäuser Boston Inc., Boston, MA, 1983.
Mathematical Reviews (MathSciNet): MR85h:14026
Zentralblatt MATH: 0509.14049
[Mu2] D. Mumford, Tata lectures on theta. II, Progress in Mathematics, vol. 43, Birkhäuser Boston Inc., Boston, MA, 1984.
Mathematical Reviews (MathSciNet): MR86b:14017
Zentralblatt MATH: 0549.14014
[P] S. J. Patterson, Book Review of The Selberg Trace Formula for $\mathrm{PSL}(2,\mathbf{R})$, by D. A. Hejhal, Bull. Amer. Math. Soc. 84 (1978), 256–260.
[P-S] R. Phillips and P. Sarnak, Geodesics in homology classes, Duke Math. J. 55 (1987/88), no. 2, 287–297.
Mathematical Reviews (MathSciNet): MR88g:58151
Zentralblatt MATH: 0642.53050
Digital Object Identifier: doi:10.1215/S0012-7094-87-05515-3
Project Euclid: euclid.dmj/1077306021
[Q] D. Kvillen, Determinants of Cauchy-Riemann operators on Riemann surfaces, Funktsional. Anal. i Prilozhen. 19 (1985), no. 1, 37–41, 96.
Mathematical Reviews (MathSciNet): MR86g:32035
Zentralblatt MATH: 0603.32016
[R-S] D. B. Ray and I. M. Singer, Analytic torsion for complex manifolds, Ann. of Math. (2) 98 (1973), 154–177.
Mathematical Reviews (MathSciNet): MR52:4344
Zentralblatt MATH: 0267.32014
Digital Object Identifier: doi:10.2307/1970909
[S1] P. Sarnak, Determinants of Laplacians, Comm. Math. Phys. 110 (1987), no. 1, 113–120.
Mathematical Reviews (MathSciNet): MR89e:58116
Zentralblatt MATH: 0618.10023
Digital Object Identifier: doi:10.1007/BF01209019
[S2] P. Sarnak, Special values of Selberg's zeta-function, Number theory, trace formulas and discrete groups (Oslo, 1987) ed. K. E. Aubert, et al., Academic Press, Boston, MA, 1989, pp. 457–465.
Mathematical Reviews (MathSciNet): MR90g:11125
Zentralblatt MATH: 0668.10037
[Sm] D.-J. Smit, String theory and algebraic geometry of moduli spaces, Comm. Math. Phys. 114 (1988), no. 4, 645–685.
Mathematical Reviews (MathSciNet): MR88m:14019
Zentralblatt MATH: 0658.14014
Digital Object Identifier: doi:10.1007/BF01229459
[V-Z] A. B. Venkov and P. G. Zograf, On analogues of the Artin factorization formulas in the spectral theory of automorphic functions connected with induced representations of Fuchsian groups, Math. USSR-Izv. 21 (1983), 435–443.
Zentralblatt MATH: 0527.10020
Digital Object Identifier: doi:10.1070/IM1983v021n03ABEH001800

2008 © Duke University Press