Vector bundles on degenerations of elliptic curves and Yang-Baxter equations

Details Vector bundles on degenerations of elliptic curves and Yang-Baxter equations Vector bundles on degenerations of elliptic curves and Yang-Baxter equations

2007-08-13

arxiv.org/abs/0708.1685v2

Mathematics

Algebraic Geometry

140 pages, extended version, some typos corrected

Scientific paper

In this paper we introduce the notion of a geometric associative r-matrix attached to a genus one fibration with a section and irreducible fibres. It allows us to study degenerations of solutions of the classical Yang-Baxter equation using the approach of Polishchuk. We also calculate certain solutions of the classical, quantum and associative Yang-Baxter equations obtained from moduli spaces of (semi-)stable vector bundles on Weierstrass cubic curves.

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