**Contemporary Mathematics**

Volume: 136;
1992;
342 pp;
Softcover

MSC: Primary 14;
Secondary 32

**Print ISBN: 978-0-8218-5143-2
Product Code: CONM/136**

List Price: $84.00

AMS Member Price: $67.20

MAA Member Price: $75.60

**Electronic ISBN: 978-0-8218-7727-2
Product Code: CONM/136.E**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

# Curves, Jacobians, and Abelian Varieties

Share this page *Edited by *
*Ron Donagi*

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

## Curves, Jacobians, and Abelian Varieties

- Contents v6 free
- Preface vii8 free
- Theta vanishings for some smooth Abelian coverings of Riemann surfaces 110 free
- The period matrix of Macbeath's curve of genus seven 3140
- The continued fraction parameter in the deformation theory of classical Schottky groups 4150
- The fibers of the Prym map 5564
- Some Riemann surfaces whose Jacobians have strange product structures 127136
- The Schottky relation in genus 4 139148
- The trisecant formula and hyperelliptic surfaces 161170
- The non-abelian Szego kernel and theta-divisor 171180
- Theta functions on the boundary of moduli space 185194
- Geometery of the fano threefold of degree 10 of the first type 209218
- 1. Preliminaries 209218
- 2. Some elementary incidences, connected with the Schubert calculus on the Grassmannian of the lines in P4 212221
- 3. The elements of X as three-tangents to the ramification hypersurface R ⊂ P4 215224
- 4. A description of the conics on X = X10 219228
- 5. The family L3 of rational normal cubic curves on X 222231
- 6. The factorfamily L30 as a determinantal variety 227236
- 7. The families L3 and L30 as zero-schemes 233242
- 8. Tangent bundle theorem for the family of rational normal cubics L3 237246
- 9. Tangent bundle theorem for the family of conics on the Fano threefold X= X10 246255
- References 253262

- Some uses of analytic torsion in the study of Weierstrass points 255264
- A problem of Narasimhan 283292
- On the reduction of Abelian integrals and a problem of H. Hopf 287296
- Normalization of the Krichever data 297306
- Splittable Jacobi varieties 305314
- Theta divisors for vector bundles 327336