Duke Mathematical Journal

Integrable discrete Schrödinger equations and a characterization of Prym varieties by a pair of quadrisecants

Samuel Grushevsky and Igor Krichever

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Abstract

We prove that Prym varieties are characterized geometrically by the existence of a symmetric pair of quadrisecant planes of the associated Kummer variety. We also show that Prym varieties are characterized by certain (new) theta-functional equations. For this purpose we construct and study a difference-differential analog of the Novikov-Veselov hierarchy

Article information

Source
Duke Math. J. Volume 152, Number 2 (2010), 317-371.

Dates
First available in Project Euclid: 31 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1270041110

Digital Object Identifier
doi:10.1215/00127094-2010-014

Mathematical Reviews number (MathSciNet)
MR2656091

Subjects
Primary: 14H40: Jacobians, Prym varieties [See also 32G20]
Secondary: 37K10: Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)

Citation

Grushevsky, Samuel; Krichever, Igor. Integrable discrete Schrödinger equations and a characterization of Prym varieties by a pair of quadrisecants. Duke Math. J. 152 (2010), no. 2, 317--371. doi:10.1215/00127094-2010-014. https://projecteuclid.org/euclid.dmj/1270041110.


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