arXiv subjects

Vanja Zuliani

Publications and source records attributed to Vanja Zuliani.

5 recordsLinked to original sources

arXiv2026

Stability conditions supported on Lefschetz classes

Recently, C. Li constructed stability conditions on the derived categories of all smooth complex projective varieties. These stability conditions satisfy the support property of Kontsevich-Soibelman with respect to the lattice in cohomology generated by powers of an ample class. We extend Li's results to construct stability conditions with full support on Lefschetz type varieties whose algebraic cohomology is generated by divisor classes. This includes all smooth complex projective varieties of dimension at most 3 and smooth projective toric varieties.

math.AG↗

arXiv2026

On moduli spaces of vector bundles on $K3^{[n]}$-type IHS manifolds

We study moduli spaces of modular vector bundles on projective irreducible holomorphic symplectic manifolds of $K3^{[n]}$-type. Under suitable numerical assumptions, we exhibit connected components of these moduli spaces which are again irreducible holomorphic symplectic manifolds of $K3^{[n]}$-type. Moreover, the corresponding universal families induce derived equivalences with the original manifolds. This produces smooth components of moduli spaces of modular vector bundles on irreducible holomorphic symplectic manifolds of any even dimension.

math.AG↗

arXiv2026

Toward the noncommutative minimal model program for Fano varieties

We study the noncommutative minimal model program, as proposed by Halpern-Leistner, for Fano varieties. We construct lifts of Iritani's quantum cohomology central charge in the following examples: Grassmannians, smooth quadrics, and smooth cubic threefolds and fourfolds. Moreover, we verify that these lifted paths are quasi-convergent and give rise to the expected semiorthogonal decompositions of the bounded derived category. We also construct geometric stability conditions in the examples above and observe that, after suitable isomonodromic deformation of the quantum cohomology central charge, the quasi-convergent paths for Grassmannians and quadrics can be chosen to start in the geometric region.

math.AG↗

arXiv2025

Hodge numbers of a Fano eightfold of K3 type

We construct an explicit semistable degeneration of a Fano eightfold of index three and deduce its Hodge numbers, in particular we show that it has Picard rank one. The Fano variety is of K3 type and it is defined as a connected component of the fixed locus of a suitable antisymplectic involution on a projective variety that is deformation equivalent to the Hilbert scheme of eight points on a K3 surface. We also obtain a description of a projective model of the Hilbert square of a K3 surface of genus eight in terms of secant lines to the surface.

math.AG↗

arXiv2024

Semiorthogonal decompositions of projective spaces from small quantum cohomology

In a recent article Halpern-Leistner defines the notion of quasi--convergent path in the space of Bridgeland stability conditions. Such a path induces a semiorthogonal decomposition of the derived category. We investigate quasi-convergent paths in the stability manifold of projective spaces and answer positively to two questions posed by Halpern-Leistner. We construct quasi-convergent paths that start from the geometric region of the stability space and whose central charge is given by a fundamental solution of the quantum differential equation. We also construct quasi-convergent paths whose central charges are the quantum cohomology central charges defined by Iritani.

math.AG↗