Moduli of Double EPW-Sextics
Share this pageKieran G. O’Grady
The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of \(\bigwedge^3{\mathbb C}^6\) modulo the natural action of \(\mathrm{SL}_6\), 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. 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.
Table of Contents
Table of Contents
Moduli of Double EPW-Sextics
- Cover Cover11
- Title page i2
- Chapter 0. Introduction 112
- Chapter 1. Preliminaries 718
- Chapter 2. One-parameter subgroups and stability 1324
- Chapter 3. Plane sextics and stability of lagrangians 3142
- Chapter 4. Lagrangians with large stabilizers 4960
- Chapter 5. Description of the GIT-boundary 5970
- Chapter 6. Boundary components meeting ℑ in a subset of 𝔛_{𝒲}∪{𝔵,𝔵^{∨}} 6576
- Chapter 7. The remaining boundary components 107118
- 7.1. \gB_{\cF₂} 107118
- 7.2. \gB_{\cF₂}∩\gI 111122
- 7.2.1. Set-up and statement of the main results 111122
- 7.2.2. The 3-fold swept out by the projective planes parametrized by 𝑖₊(𝐷) 112123
- 7.2.3. Explicit description of \WW^{𝜓}_{𝑓𝑖𝑥}. 113124
- 7.2.4. \gX_{\cV} is irreducible of dimension 3 114125
- 7.2.5. Points of \gB_{\cF₂}∩\gI are represented by lagrangians in \WW^{𝜓}_{𝑓𝑖𝑥} 119130
- 7.2.6. 𝐶_{𝑊,𝐴} for 𝐴∈\XX^{𝜓}_{\cV} and 𝑊 spanned by 𝛼∈𝑉₀₁, 𝛽∈𝑉₂₃ and 𝛾∈𝑉₄₅ 123134
- 7.2.7. Proof that \gB_{\cF₂}∩\gI=\gX_{\cV} 129140
- 7.3. \gX_{\cN₃} 129140
- 7.4. \gX_{\cN₃}∩\gI 132143
- Appendix A. Elementary auxiliary results 149160
- Appendix B. Tables 155166
- Bibliography 171182
- Back Cover Back Cover1188