13 citations · 38 across the 20 of their papers we have counts for
22 papers
Bloch's conjecture for (anti-)autoequivalences on K3 surfaces
Zhiyuan Li, Xun Yu, Ruxuan Zhang
In this paper, we investigate Bloch's conjecture for autoequivalence on K3 surfaces. We introduce the notion of reflective autoequivalence of twisted K3 surfaces and prove Bloch's…
Mukai's program for non-primitive curves on K3 surfaces
Yiran Cheng, Zhiyuan Li, Haoyu Wu
Mukai's program seeks to recover a K3 surface from any curve on it by exhibiting it as a Fourier-Mukai partner to a Brill-Noether locus of vector bundles on the curve. In t…
Unpolarized Shafarevich conjectures for hyper-Kähler varieties
Lie Fu, Zhiyuan Li, Teppei Takamatsu +1
The Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collecti…
Deligne-Beilinson cohomology of the universal K3 surface
Zhiyuan Li, Xun Zhang
O'Grady's generalized Franchetta conjecture (GFC) is concerned with codimension 2 algebraic cycles on universal polarized K3 surfaces. In \cite{BL17}, this conjecture has been stud…
Beauville-Voisin filtrations on zero cycles of moduli space of stable sheaves on K3 surfaces
Zhiyuan Li, Ruxuan Zhang
The Beauville-Voisin conjecture predicts the existence of a filtration on projective hyper-Kähler manifolds opposite to the conjecture Bloch-Beilinson filtration, called the Beauiv…
Unpolarized Shafarevich conjectures for hyper-Kähler varieties
Lie Fu, Zhiyuan Li, Haitao Zou
Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collection o…
Algebraic reverse Khovanskii--Teissier inequality via Okounkov bodies
Chen Jiang, Zhiyuan Li
Let be a projective variety of dimension over an algebraically closed field of arbitrary characteristic and let be nef divisors on . We show that for any integ…
Derived isogenies and isogenies for abelian surfaces
Zhiyuan Li, Haitao Zou
In this paper, we study the twisted Fourier-Mukai partners of abelian surfaces. Following the work of Huybrechts [doi:10.4171/CMH/465], we introduce the twisted derived equivalence…
A note on Fourier-Mukai partners of abelian varieties over positive characteristic fields
Zhiyuan Li, Haitao Zou
Over complex numbers, the Fourier-Mukai partners of abelian varieties are well-understood. A celebrated result is Orlov's derived Torelli theorem. In this note, we study the FM-par…
Tautological classes of hyper-Kähler manifolds. Erratum
Nicolas Bergeron, Zhiyuan Li
This note is an erratum to the paper "Tautological classes on moduli spaces of hyper-Kähler manifolds." Thorsten Beckman and Mirko Mauri have pointed to us a gap in the proof of \c…
Supersingular O'Grady varieties of dimension six
Lie Fu, Zhiyuan Li, Haitao Zou
O'Grady constructed a 6-dimensional irreducible holomorphic symplectic variety by taking a crepant resolution of some moduli space of stable sheaves on an abelian surface. In this…
P=W for Lagrangian fibrations and degenerations of hyper-Kähler manifolds
Andrew Harder, Zhiyuan Li, Junliang Shen +1
We identify the perverse filtration of a Lagrangian fibration with the monodromy weight filtration of a maximally unipotent degeneration of compact hyper-Kähler manifolds.
Supersingular irreducible symplectic varieties
Lie Fu, Zhiyuan Li
We study symplectic varieties defined over fields of positive characteristics, especially the supersingular ones, generalizing the theory of supersingular K3 surfaces. In this work…
Asymptotic Chow stability of toric Del Pezzo surfaces
King-Leung Lee, Zhiyuan Li, Jacob Sturm +1
In this short note, we study the asymptotic Chow polystability of toric Del Pezzo surfaces appear in the moduli space of Kähler-Einstein Fano varieties constructed in [OSS16].
Tautological classes on moduli space of hyperkähler manifolds
Nicolas Bergeron, Zhiyuan Li
In this paper, we discuss the cycle theory on moduli spaces $\cF_h$ of -polarized hyperkähler manifolds. Firstly, we construct the tautological ring on $\cF_h$ following the wor…
The Noether-Lefschetz conjecture and generalizations
Nicolas Bergeron, Zhiyuan Li, John Millson +1
We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree…
Picard groups on moduli of K3 surfaces with Mukai models
Francois Greer, Zhiyuan Li, Zhiyu Tian
We discuss the Picard group of moduli space of quasi-polarized K3 surfaces of genus and . In this range, is unirational and a g…
Integral Hodge classes on fourfolds fiberd by quadric bundles
Zhiyuan Li, Zhiyu Tian
We discuss the space of sections and certain bisections on a quadric surfaces bundle over a smooth curve. The Abel-Jacobi from these spaces to the intermediate Jacobian will be…
On Rational Connectedness of Globally F-Regular Threefolds
Yoshinori Gongyo, Zhiyuan Li, Zsolt Patakfalvi +3
In this paper, we show that projective globally -regular threefolds, defined over an algebraically closed field of characteristic , are rationally chain connected.
Moduli space of quasi-polarized K3 surfaces of degree 6 and 8
Zhiyuan Li, Zhiyu Tian
In this paper, we study the moduli space of quasi-polarized complex K3 surfaces of degree 6 and 8 via geometric invariant theory. The general members in such moduli spaces are comp…
Modular Forms and Special Cubic Fourfolds
Zhiyuan Li, Letao Zhang
We study the degree of the special cubic fourfolds in the Hilbert scheme of cubic fourfolds via a computation of the generating series of Heegner divisors of even lattice of signat…
Sections of Calabi-Yau threefolds with K3 fibration
Zhiyuan Li
We study sections of a Calabi-Yau threefold fibered over a curve by K3 surfaces. We show that there exist infinitely many isolated sections on certain K3 fibered Calabi-Yau threefo…