9 papers · 1 filter
Topology of Galois conjugate character varieties
Junliang Shen, Siqing Zhang
We study the interaction between integral structures, automorphisms, and tautological relations for the cohomology of character varieties. Based on this, we propose a method to det…
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…
Cohomology of compactified Jacobians for locally planar integral curves
Junliang Shen
This article surveys some recent developments on the cohomology of the compactified Jacobian associated with a locally planar integral curve. Topics discussed here include the Ngô…
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…