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Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces

Part of: Surfaces and higher-dimensional varieties Birational geometry

Published online by Cambridge University Press:  11 August 2009

Brendan Hassett  and
Yuri Tschinkel
Brendan Hassett
Affiliation:
Department of Mathematics, Rice University, 6100 South Main Street, Houston, TX 77251-1892, USA (hassett@rice.edu)
Yuri Tschinkel
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA (tschinkel@cims.nyu.edu)
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Abstract

We study the birational geometry of irreducible holomorphic symplectic varieties arising as varieties of lines of general cubic fourfolds containing a cubic scroll. We compute the ample and moving cones, and exhibit a birational automorphism of infinite order explaining the chamber decomposition of the moving cone.

Keywords

holomorphic symplectic varietiescones of ample and moving divisorsbirational automorphisms

MSC classification

Secondary: 14E07: Birational automorphisms, Cremona group and generalizations 14E30: Minimal model program (Mori theory, extremal rays) 14J35: $4$-folds
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 1 , January 2010 , pp. 125 - 153
Copyright
Copyright © Cambridge University Press 2010

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