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Curves, Jacobians, and Abelian Varieties
Edited by: Ron Donagi
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Contemporary Mathematics
1992; 342 pp; softcover
Volume: 136
ISBN-10: 0-8218-5143-8
ISBN-13: 978-0-8218-5143-2
List Price: US$75
Member Price: US$60
Order Code: CONM/136
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This volume contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on the Schottky Problem, held in June 1990 at the University of Massachusetts at Amherst. The conference explored various aspects of the Schottky problem of characterizing Jacobians of curves among all abelian varieties. Some of the articles study related themes, including the moduli of stable vector bundles on a curve, Prym varieties and intermediate Jacobians, and special Jacobians with exotic polarizations or product structures.

Readership

Researchers interested in algebraic geometry, Riemann surfaces, and theta functions.

Table of Contents

  • R. D. M. Accola -- Theta vanishings for some smooth Abelian coverings of Riemann surfaces
  • K. Berry and M. Tretkoff -- The period matrix of Macbeath's curve of genus seven
  • R. Brooks -- The continued fraction parameter in the deformation theory of classical Schottky groups
  • R. Donagi -- The fibers of the Prym map
  • C. J. Earle -- Some Riemann surfaces whose Jacobians have strange product structures
  • L. Ehrenpreis -- The Schottky relation in genus \(4\)
  • H. M. Farkas -- The trisecant formula and hyperelliptic surfaces
  • J. Fay -- The non-abelian Szegö kernel and theta-divisor
  • G. G. Díez -- Theta functions on the boundary of moduli space
  • A. I. Iliev -- Geometry of the fano threefold of degree 10 of the first type
  • J. Jorgenson -- Some uses of analytic torsion in the study of Weierstrass points
  • G. R. Kempf -- A problem of Narasimhan
  • H. H. Martens -- On the reduction of Abelian integrals and a problem of H. Hopf
  • M. Mulase -- Normalization of the Krichever data
  • J. F. X. Ries -- Splittable Jacobi varieties
  • M. Teixidor-I-Bigas and L. W. Tu -- Theta divisors for vector bundles
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