Reduction of divisors and Kowalevski top

TL;DR

This paper constructs reduced divisors on elliptic curves associated with the Kowalevski top, clarifying the algebraic geometric structure underlying its integrability.

Contribution

It explicitly constructs reduced divisors for the elliptic curves related to the Kowalevski top, advancing the algebraic geometric understanding of its integrable structure.

Findings

Explicit construction of reduced divisors on elliptic curves

Clarification of the algebraic geometric structure of Kowalevski top

Enhanced understanding of the divisor classes in integrable systems

Abstract

In the modern theory of the Kowalevski top there are two elliptic curves introduced by Kowalevski and by Reyman and Semenov-Tian-Shansky. The Kowalevski variables of separation and poles of the Baker-Akhiezer function define two classes of linearly equivalent divisors on these elliptic curves. According to the Riemann-Roch theorem each class has a unique reduced representative and we construct such reduced divisors for the Kowalevski top.