7 citations · 13 across the 7 of their papers we have counts for
17 papers · 1 filter
-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…
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…
Hilbert squares of degeneracy loci
Enrico Fatighenti, Francesco Meazzini, Giovanni Mongardi +1
Let be the first degeneracy locus of a morphism of vector bundles corresponding to a general matrix of linear forms in . We prove that, under certain positivity c…
Deformations of rational curves on primitive symplectic varieties and applications
Christian Lehn, Giovanni Mongardi, Gianluca Pacienza
We study the deformation theory of rational curves on primitive symplectic varieties and show that if the rational curves cover a divisor, then, as in the smooth case, they deform…
Gushel-Mukai varieties with many symmetries and an explicit irrational Gushel-Mukai threefold
Olivier Debarre, Giovanni Mongardi
We construct an explicit complex smooth Fano threefold with Picard number 1, index 1, and degree 10 (also known as a Gushel-Mukai threefold) and prove that it is not rational by sh…
Birational geometry of irreducible holomorphic symplectic tenfolds of O'Grady type
Giovanni Mongardi, Claudio Onorati
In this paper we analyse the birational geometry of O'Grady ten dimensional manifolds, giving a characterisation of Kaehler classes and lagrangian fibrations. Moreover, we study sy…