Giulia Saccà
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View article: Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations
Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations Open
We show that the hyper‐Kähler varieties of OG10‐type constructed by Laza–Saccà–Voisin (LSV) verify the Lefschetz standard conjecture. This is an application of a more general result, stating that certain Lagrangian fibrations verify this c…
View article: Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories
Algebraic Geometry: Wall Crossing and Moduli Spaces, Varieties and Derived Categories Open
The workshop addressed a broad range of subjects in algebraic geometry. Recent results on moduli spaces of various types (of sheaves, complexes, varieties) played a prominent role in many of the talks, as well as derived categories of cohe…
View article: Compactifying Lagrangian fibrations
Compactifying Lagrangian fibrations Open
We suggest a general framework for compactifing quasi-projective Lagrangian fibrations of geometric origin by holomorphic symplectic varieties. This framework includes a compactification criterion, which we then apply to various fibrations…
View article: Irreducible symplectic varieties via relative Prym varieties
Irreducible symplectic varieties via relative Prym varieties Open
Generalizing work of Markushevich--Tikhomirov and Arbarello--Saccà--Ferretti, we use relative Prym varieties to construct Lagrangian fibered symplectic varieties in infinitely many dimensions. We then give criteria for when the constructio…
View article: The geometry of antisymplectic involutions, II
The geometry of antisymplectic involutions, II Open
We continue our study of fixed loci of antisymplectic involutions on projective hyper-Kähler manifolds of $\mathrm{K3}^{[n]}$-type induced by an ample class of square 2 in the Beauville-Bogomolov-Fujiki lattice. We prove that if the divisi…
View article: Singularities of Bridgeland moduli spaces for K3 categories: an update
Singularities of Bridgeland moduli spaces for K3 categories: an update Open
This survey is a continuation of the study undertaken in \cite{AS18}. We examine the local structure of Bridgeland moduli spaces $M_σ(v,\D)$, where the relevant triangulated category $\D$ is either the bounded derived category $\D=\D^b(X)$…
View article: Birational geometry of the intermediate Jacobian fibration of a cubic fourfold
Birational geometry of the intermediate Jacobian fibration of a cubic fourfold Open
We show that the intermediate Jacobian fibration associated to any smooth cubic fourfold $X$ admits a hyper-K\"ahler compactification $J(X)$ with a regular Lagrangian fibration $J \to \mathbb P^5$. This builds upon arXiv:1602.05534, where …
View article: Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations
Relative and absolute Lefschetz standard conjectures for some Lagrangian fibrations Open
We show that the hyper-Kähler varieties of OG10-type constructed by Laza-Saccà-Voisin (LSV) verify the Lefschetz standard conjecture. This is an application of a more general result, stating that certain Lagrangian fibrations verify this c…
View article: Birational geometry of the intermediate Jacobian fibration of a cubic fourfold
Birational geometry of the intermediate Jacobian fibration of a cubic fourfold Open
We show that the intermediate Jacobian fibration associated to any smooth cubic fourfold $X$ admits a hyper-Kähler compactification $J(X)$ with a regular Lagrangian fibration $J \to \mathbb P^5$. This builds upon arXiv:1602.05534, where th…
View article: Remarks on degenerations of hyper-Kähler manifolds
Remarks on degenerations of hyper-Kähler manifolds Open
Using the Minimal model program, any degeneration of -trivial varieties can be arranged to be in a Kulikov type form, i.e. with trivial relative canonical divisor and mild singularities. In the hyper-Kähler setting, we can then deduce a fi…
View article: The Hodge diamond of O’Grady’s six-dimensional example
The Hodge diamond of O’Grady’s six-dimensional example Open
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, thereby computing its Hodge numbers.
View article: Remarks on degenerations of hyper-K\"ahler manifolds
Remarks on degenerations of hyper-K\"ahler manifolds Open
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 the hyper-K\"ahler setting, we can then deduce a…
View article: A hyper-Kähler compactification of the intermediate Jacobian fibration associated with a cubic 4-fold
A hyper-Kähler compactification of the intermediate Jacobian fibration associated with a cubic 4-fold Open
Let $X$ be a general cubic $4$-fold. It was observed by Donagi and Markman that the relative intermediate Jacobian fibration $\\mathcal{J}_U/U$ (with $U=(\\mathbb{P}^5)^\\vee\\setminus X^\\vee$) associated with the family of smooth hyperpl…
View article: Explicit Brill–Noether–Petri general curves
Explicit Brill–Noether–Petri general curves Open
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), \Bigl(\frac{1}{4}, -\frac{33}{8} \Bigr), respectively. We pro…
View article: A hyper-Kähler compactification of the Intermediate Jacobian fibration associated to a cubic fourfold
A hyper-Kähler compactification of the Intermediate Jacobian fibration associated to a cubic fourfold Open
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 holomorphic symplectic form making the fibration La…
View article: Relative Prym varieties associated to the double cover of an Enriques surface
Relative Prym varieties associated to the double cover of an Enriques surface Open
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 $\CC\to |C|$ and $\D\to |f^*C|$ are the universal famil…
View article: Singularities of moduli spaces of sheaves on K3 surfaces and Nakajima\n quiver varieties
Singularities of moduli spaces of sheaves on K3 surfaces and Nakajima\n quiver varieties Open
The aim of this paper is to study the singularities of certain moduli spaces\nof sheaves on K3 surfaces by means of Nakajima quiver varieties. The\nsingularities in question arise from the choice of a non--generic polarization,\nwith respe…