Periods of Double EPW-sextics

Details Periods of Double EPW-sextics Periods of Double EPW-sextics

2012-03-29

arxiv.org/abs/1203.6495v1

Mathematics

Algebraic Geometry

Fourth in a series of papers on moduli and periods of double EPW-sextics. It provides motivation for the point of view adopted

Scientific paper

We study the indeterminacy locus of the period map for double EPW-sextics. We recall that double EPW-sextics are parametrized by lagrangian subspaces of the third wedge-product of a 6-dimensional complex vector-space. The indeterminacy locus is contained in the set of lagrangians containing a decomposable vector. The projectivization of the 3-dimensional support of such a decomposable vector contains a degeneracy subscheme which is either all of the plane or a sextic curve. We show that the period map is regular on any lagrangian A such that for all decomposables in A the corresponding degeneracy subscheme is a GIT-semistable sextic curve whose closure (in the semistable locus) does not contain a triple conic.

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