| eBook ISBN: | 978-1-4704-2824-2 |
| Product Code: | MEMO/240/1136.E |
| List Price: | $93.00 |
| MAA Member Price: | $83.70 |
| AMS Member Price: | $55.80 |
| eBook ISBN: | 978-1-4704-2824-2 |
| Product Code: | MEMO/240/1136.E |
| List Price: | $93.00 |
| MAA Member Price: | $83.70 |
| AMS Member Price: | $55.80 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 240; 2015; 172 ppMSC: Primary 14
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.
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Table of Contents
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Chapters
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1. Introduction
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2. Preliminaries
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3. One-parameter subgroups and stability
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4. Plane sextics and stability of lagrangians
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5. Lagrangians with large stabilizers
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6. Description of the GIT-boundary
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7. Boundary components meeting $\mathfrak {I}$ in a subset of $\mathfrak {X}_{\mathcal {W}}\cup \{\mathfrak {x},\mathfrak {x}^{\vee }\}$
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8. The remaining boundary components
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A. Elementary auxiliary results
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B. Tables
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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.
-
Chapters
-
1. Introduction
-
2. Preliminaries
-
3. One-parameter subgroups and stability
-
4. Plane sextics and stability of lagrangians
-
5. Lagrangians with large stabilizers
-
6. Description of the GIT-boundary
-
7. Boundary components meeting $\mathfrak {I}$ in a subset of $\mathfrak {X}_{\mathcal {W}}\cup \{\mathfrak {x},\mathfrak {x}^{\vee }\}$
-
8. The remaining boundary components
-
A. Elementary auxiliary results
-
B. Tables
