Geometric differential equations on bundles of Jacobians of curves of genus 1 and 2

Author:
E. Yu. Netaĭ

Translated by:
E. Khukhro

Original publication:
Trudy Moskovskogo Matematicheskogo Obshchestva, tom **74** (2013), vypusk 2.

Journal:
Trans. Moscow Math. Soc. **2013**, 281-292

MSC (2010):
Primary 53C07; Secondary 34A30, 34A34, 34A26, 33C20

Published electronically:
April 9, 2014

MathSciNet review:
3235801

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct some differential equations describing the geometry of bundles of Jacobians of algebraic curves of genus 1 and 2.

For an elliptic curve we produce differential equations on the coefficients of a cometric compatible with the Gauss-Manin connection of the universal bundle of Jacobians of elliptic curves. This cometric is defined in terms of a solution of the linear system of differential equations

For a curve of genus 2 we find differential equations defined by vector fields tangent to the discriminant of the curve. Solutions of these equations define the coefficients of matrix equations on cometrics compatible with the Gauss-Manin connection of the universal bundle of Jacobians of curves of genus 2.

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Additional Information

**E. Yu. Netaĭ**

Affiliation:
Steklov Mathematical Institute, Moscow

Email:
bunkova@mi.ras.ru

DOI:
https://doi.org/10.1090/S0077-1554-2014-00223-5

Keywords:
Elliptic curves,
hyperelliptic curves,
Gauss--Manin connection,
Meijer $G$-functions,
hypergeometric functions.

Published electronically:
April 9, 2014

Additional Notes:
This research was supported by the Russian Foundation for Basic Research (grant nos. 12-01-33058 and 11-01-00197-a) and by the grant 2010-220-01-077 of the Government of the Russian Federation, contract 11.G34.31.0005.

Article copyright:
© Copyright 2014
E. Yu.Netaĭ