Moduli of Double EPW-Sextics

ISBN-13: 9781470416966 / Angielski

Kieran G. O'Grady

Opis

The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of $igwedge^3{mathbb C}^6$ modulo the natural action of $mathrm_6$, call it $mathfrak$. This is a compactification of the moduli space of smooth double EPW-sextics and hence birational to the moduli space of HK $4$-folds of Type $K3^{[2]}$ polarized by a divisor of square $2$ for the Beauville-Bogomolov quadratic form. The author will determine the stable points. His work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic $4$-folds.

Spis treści

• Introduction
• Preliminaries
• One-parameter subgroups and stability
• Plane sextics and stability of lagrangians
• Lagrangians with large stabilizers
• Description of the GIT-boundary
• Boundary components meeting $\mathfrak$ in a subset of $\mathfrak_{\mathcal}\cup\{\mathfrak, \mathfrak^{\vee}\}$
• The remaining boundary components
• Appendix A. Elementary auxiliary results
• Appendix B. Tables
• Bibliography