collaborators

5 papers

math.AG2026

-cycles and sheaves on abelian surfaces

Giovanni Mongardi, Gianluca Pacienza, Laura Pertusi

We introduce a filtration on the Chow ring of an abelian surface , inspired by O'Grady's filtration on K3 surfaces. We give a geometric description of the filtration, and we pro…

math.AG2025

On the Zariski density of rational curves on IHS manifolds

Pietro Beri, Giovanni Mongardi, Gianluca Pacienza

In analogy with recent works on surfaces, we study the existence of infinitely many ruled divisors on projective irreducible holomorphic symplectic (IHS) manifolds. We prove s…

math.AG2025

On the Boucksom-Zariski decomposition for irreducible symplectic varieties and bounded negativity

Michał Kapustka, Giovanni Mongardi, Gianluca Pacienza +1

Zariski decomposition plays an important role in the theory of algebraic surfaces due to many applications. For irreducible symplectic manifolds Boucksom provided a characterizatio…

math.AG2025

Symplectic involutions of type and Kummer type manifolds

Ljudmila Kamenova, Giovanni Mongardi, Alexei Oblomkov

In this paper we describe the fixed locus of a symplectic involution on a hyperkähler manifold of type or of Kummer type. We prove that the fixed locus consists of…

math.AG2025

Fixed loci of symplectic automorphisms of and -Kummer type manifolds

Ljudmila Kamenova, Giovanni Mongardi, Alexei Oblomkov

The aim of this paper is to give an explicit description of the fixed loci of symplectic automorphisms for certain hyperkahler manifolds, namely for Hilbert schemes on K3 surfaces…