Geodesic
Vector bundles on plane cubic curves and the classical Yang–Baxter equation
Journal of the European Mathematical Society, Tome 17 (2015) no. 3, pp. 591-644 Cet article a éte moissonné depuis la source EMS Press

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In this article, we develop a geometric method to construct solutions of the classical Yang–Baxter equation, attaching a family of classical r-matrices to the Weierstrass family of plane cubic curves and a pair of coprime positive integers. It turns out that all elliptic r-matrices arise in this way from smooth cubic curves. For the cuspidal cubic curve, we prove that the obtained solutions are rational and compute them explicitly. We also describe them in terms of Stolin's classification and prove that they are degenerations of the corresponding elliptic solutions.
DOI : 10.4171/jems/512
Classification : 16-XX, 14-XX, 18-XX
Keywords: Yang–Baxter equations, elliptic fibrations, vector bundles on curves of genus one, derived categories, Massey products 
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     author = {Igor Burban and Thilo Henrich},
     title = {Vector bundles on plane cubic curves and the classical {Yang{\textendash}Baxter} equation},
     journal = {Journal of the European Mathematical Society},
     pages = {591--644},
     year = {2015},
     volume = {17},
     number = {3},
     doi = {10.4171/jems/512},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/512/}
}
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Igor Burban; Thilo Henrich. Vector bundles on plane cubic curves and the classical Yang–Baxter equation. Journal of the European Mathematical Society, Tome 17 (2015) no. 3, pp. 591-644. doi: 10.4171/jems/512

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