# A CLASSIFICATION OF LAGRANGIAN PLANES IN HOLOMORPHIC SYMPLECTIC VARIETIES

@article{Bakker2015ACO, title={A CLASSIFICATION OF LAGRANGIAN PLANES IN HOLOMORPHIC SYMPLECTIC VARIETIES}, author={Benjamin Bakker}, journal={Journal of the Institute of Mathematics of Jussieu}, year={2015}, volume={16}, pages={859 - 877} }

Classically, an indecomposable class $R$ in the cone of effective curves on a K3 surface $X$ is representable by a smooth rational curve if and only if $R^{2}=-2$ . We prove a higher-dimensional generalization conjectured by Hassett and Tschinkel: for a holomorphic symplectic variety $M$ deformation equivalent to a Hilbert scheme of $n$ points on a K3 surface, an extremal curve class $R\in H_{2}(M,\mathbb{Z})$ in the Mori cone is the line in a Lagrangian $n$ -plane $\mathbb{P}^{n}\subset M$ if…

## 13 Citations

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Jieao Song recently conjectured a formula for the class of a Lagrangian plane on a hyperk¨ahler variety of K 3 [ n ] -type in terms of the class of a line on it. We give a proof of this conjecture if…

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. We introduce a linearised form of the square root of the Todd class inside the Verbitsky component of a hyper-Kähler manifold using the extended Mukai lattice. This enables us to deﬁne a Mukai…

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We introduce a linearised form of the square root of the Todd class inside the Verbitsky component of a hyper-Kähler manifold using the extended Mukai lattice. This enables us to define a Mukai…

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Character formulas on cohomology of deformations of Hilbert schemes of K3 surfaces

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The graded character formula of the generic Mumford-Tate group representation on the cohomology ring of X is computed, and a generating series is derived for deducing the number of canonical Hodge classes on X.

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