17 citations · 76 across the 29 of their papers we have counts for
30 papers
Dualizable abelian fibrations
Davesh Maulik, Junliang Shen, Qizheng Yin
In his proof of the fundamental lemma of the Langlands program, Ngô initiated the study of the decomposition theorem for abelian fibrations. When an abelian fibration admits a dual…
On the Orlov conjecture for hyper-Kähler varieties via hyperholomorphic bundles
Davesh Maulik, Junliang Shen, Qizheng Yin
We study Fourier transforms induced by Markman's projectively hyperholomorphic bundles on products of hyper-Kähler varieties of -type. As applications, we prove the follo…
The intrinsic cohomology ring of the universal compactified Jacobian over the moduli space of stable curves
Younghan Bae, Davesh Maulik, Junliang Shen +1
The purpose of this paper is to study the cohomology rings of universal compactified Jacobians. Over the moduli space of Deligne-Mumford stable marke…
The period-index problem for hyper-Kähler varieties via hyperholomorphic bundles
James Hotchkiss, Davesh Maulik, Junliang Shen +2
We prove new bounds for the period-index problem for hyper-Kähler varieties of -type using projectively hyperholomorphic bundles constructed by Markman. We show that $\ma…
The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles
Davesh Maulik, Junliang Shen, Qizheng Yin +1
We show that birational hyper-Kähler varieties of -type are derived equivalent, establishing the D-equivalence conjecture in these cases. The Fourier-Mukai kernels of our…
Algebraic cycles and Hitchin systems
Davesh Maulik, Junliang Shen, Qizheng Yin
The purpose of this paper is to study motivic aspects of the Hitchin system for . Our results include the following. (a) We prove the motivic decomposition conjectur…
On generalized Beauville decompositions
Younghan Bae, Davesh Maulik, Junliang Shen +1
Motivated by the Beauville decomposition of an abelian scheme and the "Perverse = Chern" phenomenon for a compactified Jacobian fibration, we study in this paper splittings of the…
Perverse filtrations and Fourier transforms
Davesh Maulik, Junliang Shen, Qizheng Yin
We study the interaction between Fourier-Mukai transforms and perverse filtrations for a certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration…
Fourier-Mukai transforms and the decomposition theorem for integrable systems
Davesh Maulik, Junliang Shen, Qizheng Yin
We study the interplay between the Fourier-Mukai transform and the decomposition theorem for an integrable system . Our main conjecture is that the Fourier-Muka…
Perverse-Hodge complexes for Lagrangian fibrations
Junliang Shen, Qizheng Yin
Perverse-Hodge complexes are objects in the derived category of coherent sheaves obtained from Hodge modules associated with Saito's decomposition theorem. We study perverse-Hodge…
On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties
Camilla Felisetti, Junliang Shen, Qizheng Yin
We prove several results concerning the intersection cohomology and the perverse filtration associated with a Lagrangian fibration of an irreducible symplectic variety. We first sh…
Motivic decompositions for the Hilbert scheme of points of a K3 surface
Andrei Neguţ, Georg Oberdieck, Qizheng Yin
We construct an explicit, multiplicative Chow-Künneth decomposition for the Hilbert scheme of points of a K3 surface. We further refine this decomposition with respect to the actio…
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.
Topology of Lagrangian fibrations and Hodge theory of hyper-Kähler manifolds
Junliang Shen, Qizheng Yin
We establish a compact analog of the P = W conjecture. For a holomorphic symplectic variety with a Lagrangian fibration, we show that the perverse numbers associated with the fibra…
Rational curves in holomorphic symplectic varieties and Gromov-Witten invariants
Georg Oberdieck, Junliang Shen, Qizheng Yin
We use Gromov-Witten theory to study rational curves in holomorphic symplectic varieties. We present a numerical criterion for the existence of uniruled divisors swept out by ratio…
K3 categories, one-cycles on cubic fourfolds, and the Beauville-Voisin filtration
Junliang Shen, Qizheng Yin
We explore the connection between categories and 0-cycles on holomorphic symplectic varieties. In this paper, we focus on Kuznetsov's noncommutative category associated t…
Tautological classes with twisted coefficients
Dan Petersen, Mehdi Tavakol, Qizheng Yin
Let be the moduli space of smooth genus curves. We define a notion of Chow groups of with coefficients in a representation of , and we define a subgroup of…
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…
Relations in the tautological ring of the moduli space of K3 surfaces
Rahul Pandharipande, Qizheng Yin
We study the interplay of the moduli of curves and the moduli of K3 surfaces via the virtual class of the moduli spaces of stable maps. Using Getzler's relation in genus 1, we cons…
On O'Grady's generalized Franchetta conjecture
Nebojsa Pavic, Junliang Shen, Qizheng Yin
We study relative zero cycles on the universal polarized surface of degree . It was asked by O'Grady if the restriction of any class in $\mathrm{…
On the Chow ring of certain rational cohomology tori
Zhi Jiang, Qizheng Yin
Let be an abelian cover from a complex algebraic variety with quotient singularities to an abelian variety. We show that induces an isomorphism between t…
-equivalence of zero cycles on surfaces II
Qizheng Yin, Yi Zhu
Using recent developments in the theory of mixed motives, we prove that the log Bloch conjecture holds for an open smooth complex surface if the Bloch conjecture holds for its comp…
-equivalence of zero cycles on surfaces
Yi Zhu
In this paper, we study -equivalence classes of zero cycles on open complex algebraic surfaces. We prove the logarithmic version of Mumford's theorem on zero cycles a…
Curve counting on abelian surfaces and threefolds
Jim Bryan, Georg Oberdieck, Rahul Pandharipande +1
We study the enumerative geometry of algebraic curves on abelian surfaces and threefolds. In the abelian surface case, the theory is parallel to the well-developed study of the red…