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Russian–German conference on Several Complex Variables
February 28, 2012 11:30, Moscow, Steklov Mathematical Institute
 


Trisymplectic manifolds

Misha Verbitsky

Higher School of Economics
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Misha Verbitsky
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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 ${\mathbb{CP}}^3$ that are trivial along a line admits a trisymplectic structure.

Language: English

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