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Remarks on degenerations of hyper-K\"ahler manifolds
Using the Minimal Model Program, any degeneration of K-trivial varieties can be arranged to be in a Kulikov type form, i.e. with trivial relative canonical divisor and mild singularities. In theExpand
Singularities of moduli spaces of sheaves on K3 surfaces and Nakajima quiver varieties
The aim of this paper is to study the singularities of certain moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver varieties. The singularities in question arise from the choice of aExpand
The Hodge diamond of O’Grady’s six-dimensional example
We realize O’Grady’s six-dimensional example of an irreducible holomorphic symplectic (IHS) manifold as a quotient of an IHS manifold of $\text{K3}^{[3]}$ type by a birational involution, therebyExpand
Relative Prym varieties associated to the double cover of an Enriques surface
Given an Enriques surface $T$, its universal K3 cover $f: S\to T$, and a genus $g$ linear system $|C|$ on $T$, we construct the relative Prym variety $P_H=\Prym_{v, H}(\D/\CC)$, where $\CC\to |C|$Expand
A hyper-K\"ahler compactification of the Intermediate Jacobian fibration associated to a cubic fourfold
For a general cubic fourfold, it was observed by Donagi and Markman that the relative intermediate Jacobian fibration associated to the family of its hyperplane sections carries a natural holomorphicExpand
The Hodge numbers of O'Grady 10 via Ngô strings
We determine the Hodge numbers of the hyper-Kahler manifold known as O'Grady 10 by studying some related modular Lagrangian fibrations by means of a refinement of the Ngo Support Theorem.
The Euler number of hyper-K¨ahler manifolds of OG10 type
Using the Laza-Sacc\`a-Voisin construction, we give a simple proof for the fact that the Euler characteristic of a hyper-K\"ahler manifold of OG10 type is 176,904, a result previously established byExpand
Explicit Brill-Noether-Petri general curves
Let $p_1,\dots, p_9$ be the points in $\mathbb A^2(\mathbb Q)\subset \mathbb P^2(\mathbb Q)$ with coordinates $$(-2,3),(-1,-4),(2,5),(4,9),(52,375), (5234, 37866),(8, -23), (43, 282),Expand
Relative compactified Jacobians of linear systems on Enriques surfaces
We study certain moduli spaces of sheaves on Enriques surfaces thereby obtaining, in every odd dimension, new examples of Calabi--Yau manifolds. We describe the geometry (canonical bundle,Expand