Under numerical assumptions, connected components of moduli spaces of modular vector bundles on K3^{[n]}-type IHS manifolds are again IHS manifolds of K3^{[n]}-type and induce derived equivalences with the original manifolds.
Bottini, O'Grady's tenfolds from stable bundles on hyper-Kähler fourfolds, Preprint, arXiv:2411.18528 https://arxiv.org/abs/2411.18528
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
citation-role summary
method 1
citation-polarity summary
fields
math.AG 6years
2026 6verdicts
UNVERDICTED 6roles
method 1polarities
use method 1representative citing papers
Moduli spaces of slope-stable projective bundles on K3^[2]-type HK manifolds yield normalizations that are K3^[a^2+1]-type HK manifolds, with converse and induced rational Hodge isometries.
Constructs irreducible symplectic varieties of dimension 2n (2≤n≤10) with 16≤b2≤24 as non-trivial terminalisations of finite symplectic quotients of Beauville-Mukai systems on very general K3-del Pezzo double covers.
Brauer groups of smooth loci in linear systems are bounded by Z/2Z under ampleness, with application to computing Tate-Shafarevich groups for Jacobians of plane curves.
Constructs Poincaré sheaf on compactified Prym varieties for singular curves and proves Fourier-Mukai autoequivalence, with applications to motivic decomposition and perverse filtrations.
Lecture notes summarizing recent progress on hyper-Kähler varieties via Lagrangian fibrations, atomic sheaves, and derived categories.
citing papers explorer
-
On moduli spaces of vector bundles on $K3^{[n]}$-type IHS manifolds
Under numerical assumptions, connected components of moduli spaces of modular vector bundles on K3^{[n]}-type IHS manifolds are again IHS manifolds of K3^{[n]}-type and induce derived equivalences with the original manifolds.
-
HK manifolds of Type $K3^{[a^2+1]}$ as moduli spaces of projective bundles on HK manifolds of Type $K3^{[2]}$
Moduli spaces of slope-stable projective bundles on K3^[2]-type HK manifolds yield normalizations that are K3^[a^2+1]-type HK manifolds, with converse and induced rational Hodge isometries.
-
Irreducible symplectic varieties via K3-del Pezzo double covers
Constructs irreducible symplectic varieties of dimension 2n (2≤n≤10) with 16≤b2≤24 as non-trivial terminalisations of finite symplectic quotients of Beauville-Mukai systems on very general K3-del Pezzo double covers.
-
Brauer groups of smooth loci in linear systems and torsors over Jacobians of plane curves
Brauer groups of smooth loci in linear systems are bounded by Z/2Z under ampleness, with application to computing Tate-Shafarevich groups for Jacobians of plane curves.
-
Autoduality of compactified Pryms for \'etale double covers of curves with planar singularities
Constructs Poincaré sheaf on compactified Prym varieties for singular curves and proves Fourier-Mukai autoequivalence, with applications to motivic decomposition and perverse filtrations.
-
Hyper-K\"ahler varieties: Lagrangian fibrations, atomic sheaves, and categories
Lecture notes summarizing recent progress on hyper-Kähler varieties via Lagrangian fibrations, atomic sheaves, and derived categories.