9 citations · 20 across the 4 of their papers we have counts for
9 papers
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…
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…
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…