Twisted cubics on cubic fourfolds
Algebraic Geometry
2013-07-22 v2
Abstract
We construct a new twenty-dimensional family of projective eight-dimensional irreducible holomorphic symplectic manifolds: the compactified moduli space M_3(Y) of twisted cubics on a smooth cubic fourfold Y that does not contain a plane is shown to be smooth and to admit a contraction M_3(Y) -> Z(Y) to a projective eight-dimensional symplectic manifold Z(Y). The construction is based on results on linear determinantal representations of singular cubic surfaces.
Cite
@article{arxiv.1305.0178,
title = {Twisted cubics on cubic fourfolds},
author = {Christian Lehn and Manfred Lehn and Christoph Sorger and Duco van Straten},
journal= {arXiv preprint arXiv:1305.0178},
year = {2013}
}
Comments
A proof that Z(Y) is simply-connected and irreducible hyperk\"ahler has been added. A couple of typos corrected