12 citations · 33 across the 17 of their papers we have counts for
16 papers · 1 filter
Singular hermitian metrics and the decomposition theorem of Catanese, Fujita, and Kawamata
Luigi Lombardi, Christian Schnell
We prove that a torsion-free sheaf endowed with a singular hermitian metric with semi-positive curvature and satisfying the minimal extension property admits a direct-…
Irregular fibrations of derived equivalent varieties
Federico Caucci, Luigi Lombardi
We study the behavior of irregular fibrations of a variety under derived equivalence of its bounded derived category. In particular we prove the derived invariance of the existence…
Derived invariance of the Albanese relative canonical ring
Federico Caucci, Luigi Lombardi, Giuseppe Pareschi
We show the derived invariance of various geometric invariants of smooth complex projective varieties governed by the Albanese map, including the relative canonical ring and the cl…
Moving Seshadri Constants, and Coverings of Varieties of Maximal Albanese Dimension
Luca F. Di Cerbo, Luigi Lombardi
Let be a smooth projective complex variety of maximal Albanese dimension, and let be a big line bundle. We prove that the moving Seshadri constants of the pull-backs…
Derived equivalence and fibrations over curves and surfaces
Luigi Lombardi
We prove that the bounded derived category of coherent sheaves on a smooth projective complex variety reconstructs the isomorphism classes of fibrations onto smooth projective curv…
Pushforwards of pluricanonical bundles under morphisms to abelian varieties
Luigi Lombardi, Mihnea Popa, Christian Schnell
Let be a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). We show that the sheaves beco…
Derived equivalences of canonical covers of hyperelliptic and Enriques surfaces in positive characteristic
Katrina Honigs, Luigi Lombardi, Sofia Tirabassi
We prove that any Fourier--Mukai partner of an abelian surface over an algebraically closed field of positive characteristic is isomorphic to a moduli space of Gieseker-stable shea…
On the vanishing of weight one Koszul cohomology of abelian varieties
Marian Aprodu, Luigi Lombardi
In this Note we prove the vanishing of (twisted) Koszul cohomology groups of an abelian variety with values in powers of an ample line bundle. It complements the work of…
Deformations of minimal cohomology classes on abelian varieties
Luigi Lombardi, Sofia Tirabassi
We show that the infinitesimal deformations of the Brill--Noether locus attached to a smooth non-hyperelliptic curve are in one-to-one correspondence with the deformation…
Theta-regularity of curves and Brill-Noether loci
Luigi Lombardi, Wenbo Niu
We provide a bound on the -regularity of an arbitrary reduced and irreducible curve embedded in a polarized abelian variety in terms of its degree and codimension. This is an "a…
GV-subschemes and their embeddings in principally polarized abelian varieties
Luigi Lombardi, Sofia Tirabassi
We prove that the embedding of a -subscheme in a principally polarized abelian variety does not factor through any nontrivial isogeny. As an application, we present a new proof…
Derived equivalence and non-vanishing loci II
Luigi Lombardi, Mihnea Popa
We prove a few cases of a conjecture on the invariance of cohomological support loci under derived equivalence by establishing a concrete connection with the related problem of the…
Regularity of curves in abelian varieties
Luigi Lombardi, Wenbo Niu
Inspired by a theorem of Gruson-Lazarsfeld-Peskine bounding the Castelnuovo-Mumford regularity of curves in projective spaces, we bound the Theta-regularity of curves in polarized…
Derived invariants of irregular varieties and Hochschild homology
Luigi Lombardi
We study the behavior of cohomological support loci of the canonical bundle under derived equivalence of smooth projective varieties. This is achieved by investigating the derived…
Inequalities for the Hodge numbers of irregular compact Kaehler manifolds
Luigi Lombardi
Based on work of R. Lazarsfeld and M. Popa, we use the derivative complex associated to the bundle of the holomorphic p-forms to provide inequalities for all the Hodge numbers of a…
The Equations of Singular Loci of Ample Divisors on (Subvarieties of) Abelian Varieties
Luigi Lombardi, Francesco Malaspina
In this paper we consider ideal sheaves associated to the singular loci of a divisor in a linear system of an ample line bundle on a complex abelian variety. We prove an effe…