20 citations · 138 across the 26 of their papers we have counts for
26 papers
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 filtrations, Chern filtrations, and refined BPS invariants for local
Yakov Kononov, Weite Pi, Junliang Shen
We explore connections between three structures associated with the cohomology of the moduli of 1-dimensional stable sheaves on : perverse filtrations, tautological c…
The conjecture for
Davesh Maulik, Junliang Shen
We prove the conjecture for for all ranks and curves of arbitrary genus . The proof combines a strong perversity result on tautological classes w…
Generators for the cohomology ring of the moduli of one-dimensional sheaves on
Weite Pi, Junliang Shen
We explore the structure of the cohomology ring of the moduli space of stable 1-dimensional sheaves on of any degree. We obtain a minimal set of tautological generat…
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…
Cohomology of the moduli of Higgs bundles via positive characteristic
Mark Andrea de Cataldo, Davesh Maulik, Junliang Shen +1
For any two degrees coprime to the rank, we construct a family of ring isomorphisms parameterized by GSp(2g) between the cohomology of the moduli spaces of stable Higgs bundles whi…
On the intersection cohomology of the moduli of -Higgs bundles on a curve
Davesh Maulik, Junliang Shen
We explore the cohomological structure for the (possibly singular) moduli of -Higgs bundles for arbitrary degree on a genus g curve with respect to an effective divi…
Cohomological -independence for moduli of one-dimensional sheaves and moduli of Higgs bundles
Davesh Maulik, Junliang Shen
We prove that the intersection cohomology (together with the perverse and the Hodge filtrations) for the moduli space of one-dimensional semistable sheaves supported in an ample cu…
Endoscopic decompositions and the Hausel-Thaddeus conjecture
Davesh Maulik, Junliang Shen
We construct natural operators connecting the cohomology of the moduli spaces of stable Higgs bundles with different ranks and genera which, after numerical specialization, recover…
On the P=W conjecture for
Mark Andrea A. de Cataldo, Davesh Maulik, Junliang Shen
Let be a prime number. We prove that the conjecture for is equivalent to the conjecture for . As a consequence, we verify the c…
Hitchin fibrations, abelian surfaces, and the P=W conjecture
Mark Andrea A. de Cataldo, Davesh Maulik, Junliang Shen
We study the topology of Hitchin fibrations via abelian surfaces. We establish the P=W conjecture for genus curves and arbitrary rank. In higher genus and arbitrary rank, we pr…
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…
Perverse filtrations, Hilbert schemes, and the P=W conjecture for parabolic Higgs bundles
Junliang Shen, Zili Zhang
We prove de Cataldo-Hausel-Migliorini's P=W conjecture in arbitrary rank for parabolic Higgs bundles labeled by the affine Dynkin diagrams , , $\tilde{E}_…
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…
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…
Reduced Donaldson-Thomas invariants and the ring of dual numbers
Georg Oberdieck, Junliang Shen
Let be an abelian variety. We introduce -equivariant Grothendieck rings and -equivariant motivic Hall algebras, and endow them with natural integration maps to the ring o…
Curve counting on elliptic Calabi-Yau threefolds via derived categories
Georg Oberdieck, Junliang Shen
We prove the elliptic transformation law of Jacobi forms for the generating series of Pandharipande--Thomas invariants of an elliptic Calabi--Yau 3-fold over a reduced class in the…
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{…
Motivic classes of generalized Kummer schemes via relative power structures
Andrew Morrison, Junliang Shen
We develop a power structure over the Grothendieck ring of varieties relative to an abelian monoid, which allows us to compute the motivic class of the generalized Kummer scheme. W…
The Euler characteristics of generalized Kummer schemes
Junliang Shen
We compute the Euler characteristics of the generalized Kummer schemes associated to , where is an abelian variety and is a smooth quasi-projective variety. When…