3 papers
math.AG2025
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…
math.AG2025
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…
math.AG2025
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…