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Lagrangian embeddings of cubic fourfolds containing a plane

Part of: Surfaces and higher-dimensional varieties (Co)homology theory

Published online by Cambridge University Press:  23 March 2017

Genki Ouchi
Genki Ouchi*
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Tokyo 153-8914, Japan email genki.oouchi@ipmu.jp
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Abstract

We prove that a very general smooth cubic fourfold containing a plane can be embedded into an irreducible holomorphic symplectic eightfold as a Lagrangian submanifold. We construct the desired irreducible holomorphic symplectic eightfold as a moduli space of Bridgeland stable objects in the derived category of the twisted K3 surface corresponding to the cubic fourfold containing a plane.

Keywords

derived categorystability conditionirreducible holomorphic symplectic manifold

MSC classification

Primary: 14F05: Sheaves, derived categories of sheaves and related constructions 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 5 , May 2017 , pp. 947 - 972
Copyright
© The Author 2017 

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