How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

   1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

   1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

   2. Complete and sign the license agreement.

   3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2213  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046
Email: cust-serv@ams.org

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

Powered by MathJax
  Remote Access

Moduli of double EPW-sextics


About this Title

Kieran G. O’Grady

Publication: Memoirs of the American Mathematical Society
Publication Year: 2016; Volume 240, Number 1136
ISBNs: 978-1-4704-1696-6 (print); 978-1-4704-2824-2 (online)
DOI: http://dx.doi.org/10.1090/memo/1136
Published electronically: October 9, 2015
Keywords:GIT quotient, period map, hyperkähler varieties

View full volume PDF

View other years and numbers:

Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Preliminaries
  • Chapter 3. One-parameter subgroups and stability
  • Chapter 4. Plane sextics and stability of lagrangians
  • Chapter 5. Lagrangians with large stabilizers
  • Chapter 6. Description of the GIT-boundary
  • Chapter 7. Boundary components meeting $\mathfrak I$ in a subset of $\mathfrak X_\mathcal W\cup \{\mathfrak x,\mathfrak x^\vee \}$
  • Chapter 8. The remaining boundary components
  • Appendix A. Elementary auxiliary results
  • Appendix B. Tables

Abstract


We will study the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of $⋀^{3}\mathbb C^{6}$ modulo the natural action of SL$_{6}$, call it $\mathfrak M$. 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. We will determine the stable points. Our work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic $4$-folds. We will prove a result which is analogous to a theorem of Laza asserting that cubic $4$-folds with simple singularities are stable. We will also describe the irreducible components of the GIT boundary of $\mathfrak M$. Our final goal (not achieved in this work) is to understand completely the period map from $\mathfrak M$ to the Baily-Borel compactification of the relevant period domain modulo an arithmetic group. We will analyze the locus in the GIT-boundary of $\mathfrak M$ where the period map is not regular. Our results suggest that $\mathfrak M$ is isomorphic to Looijenga’s compactification associated to $3$ specific hyperplanes in the period domain.

References [Enhancements On Off] (What's this?)

American Mathematical Society