Moduli spaces of stable objects in Enriques categories

A Perry, L Pertusi, X Zhao - arXiv preprint arXiv:2305.10702, 2023 - arxiv.org
We study moduli spaces of stable objects in Enriques categories by exploiting their relation
to moduli spaces of stable objects in associated K3 categories. In particular, we settle the …

Derived categories of hearts on Kuznetsov components

C Li, L Pertusi, X Zhao - Journal of the London Mathematical …, 2023 - Wiley Online Library
We prove a general criterion that guarantees that an admissible subcategory KK of the
derived category of an abelian category is equivalent to the bounded derived category of the …

Categorical Torelli theorems: results and open problems

L Pertusi, P Stellari - Rendiconti del Circolo Matematico di Palermo Series …, 2023 - Springer
We survey some recent results concerning the so called Categorical Torelli problem. This is
to say how one can reconstruct a smooth projective variety up to isomorphism, by using the …

Kuznetsov's Fano threefold conjecture via K3 categories and enhanced group actions

A Bayer, A Perry - Journal für die reine und angewandte Mathematik …, 2023 - degruyter.com
We settle the last open case of Kuznetsov's conjecture on the derived categories of Fano
threefolds. Contrary to the original conjecture, we prove the Kuznetsov components of …

Stability conditions and moduli spaces for Kuznetsov components of Gushel–Mukai varieties

A Perry, L Pertusi, X Zhao - Geometry & Topology, 2023 - msp.org
We prove the existence of Bridgeland stability conditions on the Kuznetsov components of
Gushel–Mukai varieties, and describe the structure of moduli spaces of Bridgeland …

Lectures on non-commutative K3 surfaces, Bridgeland stability, and moduli spaces

E Macrì, P Stellari - Birational Geometry of Hypersurfaces: Gargnano del …, 2019 - Springer
We survey the basic theory of non-commutative K3 surfaces, with a particular emphasis to
the ones arising from cubic fourfolds. We focus on the problem of constructing Bridgeland …

Atomic sheaves on hyper-K\" ahler manifolds via Bridgeland moduli spaces

H Guo, Z Liu - arXiv preprint arXiv:2406.19361, 2024 - arxiv.org
In this paper, we provide new examples of 1-obstructed and atomic sheaves on an infinite
series of locally complete families of projective hyper-K\" ahler manifolds. More precisely,(1) …

Conics on Gushel-Mukai fourfolds, EPW sextics and Bridgeland moduli spaces

H Guo, Z Liu, S Zhang - arXiv preprint arXiv:2203.05442, 2022 - arxiv.org
We identify the double dual EPW sextic $\widetilde {Y} _ {A^{\perp}} $ and the double EPW
sextic $\widetilde {Y} _A $, associated with a very general Gushel-Mukai fourfold $ X $, with …

GLSM realizations of maps and intersections of Grassmannians and Pfaffians

A Căldăraru, J Knapp, E Sharpe - Journal of High Energy Physics, 2018 - Springer
A bstract In this paper we give gauged linear sigma model (GLSM) realizations of a number
of geometries not previously presented in GLSMs. We begin by describing GLSM …

Gushel-mukai varieties

O Debarre - arXiv preprint arXiv:2001.03485, 2020 - arxiv.org
Gushel-Mukai varieties are smooth (complex) dimensionally transverse intersections of a
cone over the Grassmannian Gr (2, 5) with a linear space and a quadratic hypersurface …