MS Seminar (Mathematics - String Theory)

Speaker: Misha Verbitsky (IPMU)
Title: Trisymplectic manifolds
Date: Thu, Jan 19, 2012, 15:30 - 17:00
Place: Seminar Room A
Abstract: A trisymplectic structure on a complex 2n-manifold is a triple of holomorphic symplectic forms such that any linear combination of these forms has rank 2n, n or 0. We show that a trisymplectic manifold is equipped with a holomorphic 3-web and the Chern connection of this 3-web is holomorphic, torsion-free, and preserves the three symplectic forms. We construct a trisymplectic structure on the moduli of regular rational curves in the twistor space of a hyperkaehler manifold. We show that the moduli space $M$ of holomorphic vector bundles on $CP^3$ that are trivial along a line admits a trisymplectic structure.