In this paper the authors introduce the notion of a geometric associative \(r\)-matrix attached to a genus one fibration with a section and irreducible fibres. It allows them to study degenerations of solutions of the classical Yang-Baxter equation using the approach of Polishchuk. They 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.

Table of Contents

• Introduction
• Yang-Baxter equations
• Massey products and AYBE--a single curve
• Massey products and AYBE--families of curves
• Explicit calculations--smooth curves
• Explicit calculations--singular curves
• Summary
• Bibliography