Nuova ricerca

Camilla FELISETTI

Ricercatore t.d. art. 24 c. 3 lett. B
Dipartimento di Scienze Fisiche, Informatiche e Matematiche sede ex-Matematica


Home | Curriculum(pdf) | Didattica |


Pubblicazioni

2024 - O’Grady tenfolds as moduli spaces of sheaves [Articolo su rivista]
Felisetti, Camilla; Giovenzana, Franco; Grossi, Annalisa
abstract

We give a lattice-theoretic characterization for a manifold of $\operatorname {\mathrm {OG10}}$ type to be birational to some moduli space of (twisted) sheaves on a K3 surface. We apply it to the Li-Pertusi-Zhao variety of $\operatorname {\mathrm {OG10}}$ type associated to any smooth cubic fourfold. Moreover, we determine when a birational transformation is induced by an automorphism of the K3 surface, and we use this to classify all induced birational symplectic involutions.


2024 - On Generalized Nefness and Bigness in Adjunction Theory [Articolo su rivista]
Felisetti, Camilla; Fontanari, Claudio
abstract

We investigate effectiveness and ampleness of adjoint divisors of the form aL + bKX, where L is a suitably positive line bundle on a smooth projective variety X and a, b are positive integers.


2024 - P=W phenomena in algebraic and enumerative geometry [Articolo su rivista]
Felisetti, C.
abstract

In view of the recent proofs of the P=W conjecture, the present paper reviews and relates the latest results in the field, with a view on how P=W phenomena appear in multiple areas of algebraic geometry. As an application, we give a detailed sketch of the proof of P=W by Maulik, Shen and Yin.


2023 - INTERSECTION COHOMOLOGY OF THE MODULI SPACE OF HIGGS BUNDLES ON A GENUS 2 CURVE [Articolo su rivista]
Felisetti, Camilla
abstract


2022 - Betti numbers of Brill–Noether varieties on a general curve [Articolo su rivista]
Felisetti, Camilla; Fontanari, Claudio
abstract

We compute the rational cohomology groups of the smooth Brill–Noether varieties Gr d .C /, parametrizing linear series of degree d and dimension exactly r on a general curve C. As an application, we determine the whole intersection cohomology of the singular Brill–Noether loci W r d .C /, parametrizing complete linear series on C of degree d and dimension at least r.


2022 - On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties [Articolo su rivista]
Felisetti, C.; Shen, J.; Yin, Q.
abstract

We prove several results concerning the intersection cohomology and the perverse filtration associated with a Lagrangian fibration of an irreducible symplectic variety. We first show that the perverse numbers only depend on the deformation equivalence class of the ambient variety. Then we compute the border of the perverse diamond, which further yields a complete description of the intersection cohomology of the Lagrangian base and the invariant cohomology classes of the fibers. Lastly, we identify the perverse and Hodge numbers of intersection cohomology when the irreducible symplectic variety admits a symplectic resolution. These results generalize some earlier work by the second and third authors in the nonsingular case.


2022 - On the splitting principle of Beniamino Segre [Articolo su rivista]
Felisetti, Camilla; Fontanari, Claudio
abstract


2022 - P=W conjectures for character varieties with symplectic resolution [Articolo su rivista]
Felisetti, Camilla; Mauri, Mirko
abstract

We establish P=W and PI=WI conjectures for character varieties with structural group GLn and SLn which admit a symplectic resolution, i.e., for genus 1 and arbitrary rank, and genus 2 and rank 2. We formulate the P=W conjecture for a resolution, and prove it for symplectic resolutions. We exploit the topology of birational and quasi-étale modifications of Dolbeault moduli spaces of Higgs bundles. To this end, we prove auxiliary results of independent interest, like the construction of a relative compactification of the Hodge moduli space for reductive algebraic groups, and the projectivity of the compactification of the de Rham moduli space. In particular, we study in detail a Dolbeault moduli space which is a specialization of the singular irreducible holomorphic symplectic variety of type O’Grady 6. Résumé (Les conjectures P=W pour les variétés de caractères ayant une résolution symplectique) On établit les conjectures P=W et PI=WI pour les variétés de caractères avec groupe structurel GLn et SLn qui admettent une résolution symplectique, c’est-à-dire pour le genre 1 en rang arbitraire, et le genre 2 en rang 2. On formule la conjecture P=W pour une résolution et on la prouve pour les résolutions symplectiques. Pour la démonstration on fait appel à la topologie des modifications birationnelles et quasi-étales des espaces de modules de fibrés de Higgs. Pour cela, on démontre des résultats auxiliaires d’intérêt indépendant, comme la construction d’une compactification relative de l’espace de modules de Hodge pour les groupes algébriques réductifs, ou la théorie de l’intersection de certains cycles lagrangiens singuliers. En particulier, on étudie en détail un espace de modules des fibrés de Higgs qui est une spécialisation de la variété symplectique holomorphe irréductible singulière de type O’Grady 6.


2021 - A support theorem for nested Hilbert schemes of planar curves [Articolo su rivista]
Felisetti, Camilla
abstract

Consider a family of integral complex locally planar curves. We show that under some assumptions on the base, the relative nested Hilbert scheme is smooth. In this case, the decomposition theorem of Beilinson, Bernstein and Deligne asserts that the pushforward of the constant sheaf on the relative nested Hilbert scheme splits as a direct sum of shifted semisimple perverse sheaves. We will show that no summand is supported in positive codimension.


2018 - Two applications of the decomposition theorem to moduli spaces [Working paper]
Felisetti, Camilla
abstract