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Book DetailsContemporary MathematicsVolume: 136; 1992; 342 ppMSC: Primary 14; Secondary 32;
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.
ReadershipResearchers interested in algebraic geometry, Riemann surfaces, and theta functions.

Table of Contents

Articles

Robert D. M. Accola  Theta vanishings for some smooth abelian coverings of Riemann surfaces [ MR 1188191 ]

Kevin Berry and Marvin Tretkoff  The period matrix of Macbeath’s curve of genus seven [ MR 1188192 ]

Robert Brooks  The continued fraction parameter in the deformation theory of classical Schottky groups [ MR 1188193 ]

Ron Donagi  The fibers of the Prym map [ MR 1188194 ]

Clifford J. Earle  Some Riemann surfaces whose Jacobians have strange product structures [ MR 1188195 ]

Leon Ehrenpreis  The Schottky relation in genus $4$ [ MR 1188196 ]

Hershel M. Farkas  The trisecant formula and hyperelliptic surfaces [ MR 1188197 ]

John Fay  The nonabelian Szegő kernel and thetadivisor [ MR 1188198 ]

Gabino González Díez  Theta functions on the boundary of moduli space [ MR 1188199 ]

Atanas Iliev Iliev  Geometry of the Fano threefold of degree $10$ of the first type [ MR 1188200 ]

Jay Jorgenson  Some uses of analytic torsion in the study of Weierstrass points [ MR 1188201 ]

George R. Kempf  A problem of Narasimhan [ MR 1188202 ]

Henrik H. Martens  On the reduction of Abelian integrals and a problem of H. Hopf [ MR 1188203 ]

Motohico Mulase  Normalization of the Krichever data [ MR 1188204 ]

John F. X. Ries  Splittable Jacobi varieties [ MR 1188205 ]

Montserrat Teixidor i Bigas and Loring W. Tu  Theta divisors for vector bundles [ MR 1188206 ]


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

Articles

Robert D. M. Accola  Theta vanishings for some smooth abelian coverings of Riemann surfaces [ MR 1188191 ]

Kevin Berry and Marvin Tretkoff  The period matrix of Macbeath’s curve of genus seven [ MR 1188192 ]

Robert Brooks  The continued fraction parameter in the deformation theory of classical Schottky groups [ MR 1188193 ]

Ron Donagi  The fibers of the Prym map [ MR 1188194 ]

Clifford J. Earle  Some Riemann surfaces whose Jacobians have strange product structures [ MR 1188195 ]

Leon Ehrenpreis  The Schottky relation in genus $4$ [ MR 1188196 ]

Hershel M. Farkas  The trisecant formula and hyperelliptic surfaces [ MR 1188197 ]

John Fay  The nonabelian Szegő kernel and thetadivisor [ MR 1188198 ]

Gabino González Díez  Theta functions on the boundary of moduli space [ MR 1188199 ]

Atanas Iliev Iliev  Geometry of the Fano threefold of degree $10$ of the first type [ MR 1188200 ]

Jay Jorgenson  Some uses of analytic torsion in the study of Weierstrass points [ MR 1188201 ]

George R. Kempf  A problem of Narasimhan [ MR 1188202 ]

Henrik H. Martens  On the reduction of Abelian integrals and a problem of H. Hopf [ MR 1188203 ]

Motohico Mulase  Normalization of the Krichever data [ MR 1188204 ]

John F. X. Ries  Splittable Jacobi varieties [ MR 1188205 ]

Montserrat Teixidor i Bigas and Loring W. Tu  Theta divisors for vector bundles [ MR 1188206 ]