# 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}
}
• Benjamin Bakker
• Published 23 October 2013
• Mathematics
• Journal of the Institute of Mathematics of Jussieu
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…
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