49 citations · 138 across the 20 of their papers we have counts for
23 papers · 1 filter
Generalized Bogomolov--Gieseker inequalities via Frobenius
Chunyi Li, Zhiyu Liu, Alexander Perry +1
We establish a Bogomolov--Gieseker-type inequality for tilt-semistable objects on smooth projective varieties of dimension , in the spirit of the Bayer--Macrì--Toda conject…
Stability conditions and moduli spaces on projective families
Chunyi Li, Zhiyu Liu, Ziqi Liu +4
We extend the construction of stability conditions on projective schemes over a field to projective families over an arbitrary base, and prove that they admit proper relative modul…
Stability conditions on products of curves and Hilbert schemes of surfaces
Chunyi Li, Emanuele Macrì, Alexander Perry +2
We prove that stability conditions on the derived category of a product of curves of positive genus are uniquely determined by their central charge and the phase of skyscraper shea…
Higher dimensional moduli spaces on Kuznetsov components of Fano threefolds
Chunyi Li, Yinbang Lin, Laura Pertusi +1
We study moduli spaces of stable objects in the Kuznetsov components of Fano threefolds. We prove a general non-emptiness criterion for moduli spaces, which applies to the cases of…
Fully faithful functors, skyscraper sheaves, and birational equivalence
Chunyi Li, Xun Lin, Xiaolei Zhao
Let and be two smooth projective varieties such that there is a fully faithful exact functor from to . We show that and …
Some remarks about deformation theory and formality conjecture
Huachen Chen, Laura Pertusi, Xiaolei Zhao
Using the algebraic criterion proved by Bandiera, Manetti and Meazzini, we show the formality conjecture for universally gluable objects with linearly reductive automorphism groups…
Moduli spaces of stable objects in Enriques categories
Alexander Perry, Laura Pertusi, Xiaolei Zhao
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 settl…
On the Tate conjecture for divisors on varieties with in positive characteristics
Paul Hamacher, Ziquan Yang, Xiaolei Zhao
We prove that the Tate conjecture for divisors is ''generically true'' for mod p reductions of complex projective varieties with , under a mild assumption on moduli.…
Derived categories of hearts on Kuznetsov components
Chunyi Li, Laura Pertusi, Xiaolei Zhao
We prove a general criterion which guarantees that an admissible subcategory of the derived category of an abelian category is equivalent to the bounded derived categ…
A Refined Derived Torelli Theorem for Enriques surfaces, II: the non-generic case
Chunyi Li, Paolo Stellari, Xiaolei Zhao
We prove that two Enriques surfaces defined over an algebraically closed field of characteristic different from are isomorphic if their Kuznetsov components are equivalent. Thi…
Stability manifolds of varieties with finite Albanese morphisms
Lie Fu, Chunyi Li, Xiaolei Zhao
For a smooth projective complex variety whose Albanese morphism is finite, we show that every Bridgeland stability condition on its bounded derived category of coherent sheaves is…
Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations
Chunyi Li, Laura Pertusi, Xiaolei Zhao
For a smooth cubic fourfold Y, we study the moduli space M of semistable objects of Mukai vector in the Kuznetsov component of Y. We show that with a certain choice of…
Stability conditions and moduli spaces for Kuznetsov components of Gushel-Mukai varieties
Alexander Perry, Laura Pertusi, Xiaolei Zhao
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 semistabl…
A refined Derived Torelli Theorem for Enriques surfaces
Chunyi Li, Howard Nuer, Paolo Stellari +1
We prove that two general Enriques surfaces defined over an algebraically closed field of characteristic different from are isomorphic if their Kuznetsov components are equival…
Period integrals and Hodge modules
Laure Flapan, Robin Walters, Xiaolei Zhao
We define a map attached to any polarized Hodge module such that the restriction of to a locus on which is a variation of Hodge structures i…
Twisted cubics on cubic fourfolds and stability conditions
Chunyi Li, Laura Pertusi, Xiaolei Zhao
We give an interpretation of the Fano variety of lines on a cubic fourfold and of the hyperkahler eightfold, constructed by Lehn, Lehn, Sorger and van Straten from twisted cubic cu…
On the group of zero-cycles of holomorphic symplectic varieties
Alina Marian, Xiaolei Zhao
For a moduli space of Bridgeland-stable objects on a K3 surface, we show that the Chow class of a point is determined by the Chern class of the corresponding object on the surface.…
Derived categories of K3 surfaces, O'Grady's filtration, and zero-cycles on holomorphic symplectic varieties
Junliang Shen, Qizheng Yin, Xiaolei Zhao
Moduli spaces of stable objects in the derived category of a surface provide a large class of holomorphic symplectic varieties. In this paper, we study the interplay between C…
Smoothness and Poisson structures of Bridgeland moduli spaces on Poisson surfaces
Chunyi Li, Xiaolei Zhao
Let X be a projective smooth holomorphic Poisson surface, in other words, whose anti-canonical divisor is effective. We show that moduli spaces of certain Bridgeland stable objects…
Bridgeland Stability Conditions on Fano Threefolds
Marcello Bernardara, Emanuele Macrì, Benjamin Schmidt +1
We show the existence of Bridgeland stability conditions on all Fano threefolds, by proving a modified version of a conjecture by Bayer, Toda, and the second author. The key techni…
Birational models of moduli spaces of coherent sheaves on the projective plane
Chunyi Li, Xiaolei Zhao
We study the birational geometry of moduli spaces of semistable sheaves on the projective plane via Bridgeland stability conditions. We show that the entire MMP of their moduli spa…
Nef cones of Hilbert schemes of points on surfaces
Barbara Bolognese, Jack Huizenga, Yinbang Lin +4
Let X be a smooth projective surface of irregularity 0. The Hilbert scheme of n points on X parameterizes zero-dimensional subschemes of X of length n. In this paper, we discuss ge…
The MMP for deformations of Hilbert schemes of points on the projective plane
Chunyi Li, Xiaolei Zhao
We study the birational geometry of deformations of Hilbert schemes of points on the projective plane P2. We complete the picture in the paper of Daniele Arcara, Aaron Bertram, Izz…