November 2024
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Let X be an n -dimensional (smooth) intersection of two quadrics, and let be its cotangent bundle. We show that the algebra of symmetric tensors on X is a polynomial algebra in n variables. The corresponding map is a Lagrangian fibration, which admits an explicit geometric description; its general fiber is a Zariski open subset of an abelian variety, which is a quotient of a hyperelliptic Jacobian by a 2 -torsion subgroup. In dimension 3 , is the Hitchin fibration of the moduli space of rank 2 bundles with fixed determinant on a curve of genus 2 .