arXiv subjects

Lucas Li Bassi

Publications and source records attributed to Lucas Li Bassi.

4 recordsLinked to original sources

arXiv2025

Some remarks on L-equivalence for cubic fourfolds and hyper-K\"ahler manifolds

We prove that if two very general cubic fourfolds are L-equivalent then they are isomorphic, and we observe that there exist special cubic fourfolds which are L-equivalent but not isomorphic. When the cubic fourfolds are very general in certain Hassett divisors, we prove that if they are L-equivalent then they are also Fourier-Mukai partners. We also provide further examples in support of the fact that L-equivalent hyper-K\"ahler manifolds should be D-equivalent, as conjectured by Meinsma.

math.AG↗

arXiv2025

Inducing coverings on Hilbert schemes

We find an explicit geometric description of all coverings of the Hilbert square on a normal, complex, quasi-projective surface with finite fundamental group. We then apply this construction to show that if $\Sigma$ is an irreducible symplectic surface then its Hilbert square is an irreducible symplectic variety.

math.AG↗

arXiv2023

The Fano variety of lines on singular cyclic cubic fourfolds

We study the symplectic resolution of the Fano variety of lines on some singular cyclic cubic fourfolds, i.e. cubic fourfolds arising as cyclic 3:1 cover of $\mathbb{P}^4$ branched along a cubic threefold. In particular we are interested in the geometry of these varieties in the case of cyclic cubic fourfolds branched along a cubic threefold having one isolated singularity of type $A_i$ for $i=2,3,4$. On these symplectic resolutions we find a non-symplectic automorphism of order three induced by the covering automorphism.

math.AG↗

arXiv2023

GIT stable cubic threefolds and certain fourfolds of $K3^{[2]}$-type

We study the behaviour on some nodal hyperplanes of the isomorphism, described in a paper of 2019 by Boissi\`ere, Camere and Sarti, between the moduli space of smooth cubic threefolds and the moduli space of hyperk\"ahler fourfolds of $K3^{[2]}$-type with a non-symplectic automorphism of order three, whose invariant lattice has rank one and is generated by a class of square 6; along those hyperplanes the automorphism degenerates by jumping to another family. We generalize their result to singular nodal cubic threefolds having one singularity of type $A_i$ for $i=2, 3, 4$ providing birational maps between the loci of cubic threefolds where a generic element has an isolated singularity of the types $A_i$ and some moduli spaces of hyperk\"ahler fourfolds of $K3^{[2]}$-type with non-symplectic automorphism of order three belonging to different families. In order to treat the $A_2$ case, we introduce the notion of K\"ahler cone sections of $K$-type generalizing the definition of $K$-general polarized hyperk\"ahler manifolds.

math.AG↗