The conjecture for
D Maulik, J Shen - Annals of Mathematics, 2024 - projecteuclid.org
We prove the P=W conjecture for GL_n for all ranks n and curves of arbitrary genus g≥2.
The proof combines a strong perversity result on tautological classes with the curious Hard …
The proof combines a strong perversity result on tautological classes with the curious Hard …
Cohomological χ–independence for moduli of one-dimensional sheaves and moduli of Higgs bundles
D Maulik, J Shen - Geometry & Topology, 2023 - msp.org
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 …
filtrations) for the moduli space of one-dimensional semistable sheaves supported in an …
Hitchin systems: some recent advances
OK Sheinman, B Wang - arXiv preprint arXiv:2402.08385, 2024 - arxiv.org
arXiv:2402.08385v1 [math-ph] 13 Feb 2024 Page 1 arXiv:2402.08385v1 [math-ph] 13 Feb
2024 HITCHIN SYSTEMS: SOME RECENT ADVANCES OKSHEINMAN AND BIN WANG …
2024 HITCHIN SYSTEMS: SOME RECENT ADVANCES OKSHEINMAN AND BIN WANG …
Global critical chart for local Calabi–Yau threefolds
T Kinjo, N Masuda - International Mathematics Research Notices, 2024 - academic.oup.com
In this paper, we investigate Keller's deformed Calabi–Yau completion of the derived
category of coherent sheaves on a smooth variety. In particular, for an-dimensional smooth …
category of coherent sheaves on a smooth variety. In particular, for an-dimensional smooth …
Unramified covers and branes on the Hitchin system
We study the locus of the moduli space of GL (n, C)-Higgs bundles on a curve given by
those Higgs bundles obtained by pushforward under a connected unramified cover. We …
those Higgs bundles obtained by pushforward under a connected unramified cover. We …
On the P = W conjecture for
MA de Cataldo, D Maulik, J Shen - Selecta Mathematica, 2022 - Springer
Let p be a prime number. We prove that the P= W conjecture for SL p is equivalent to the P=
W conjecture for GL p. As a consequence, we verify the P= W conjecture for genus 2 and SL …
W conjecture for GL p. As a consequence, we verify the P= W conjecture for genus 2 and SL …
Algebraic cycles and Hitchin systems
D Maulik, J Shen, Q Yin - arXiv preprint arXiv:2407.05177, 2024 - arxiv.org
The purpose of this paper is to study motivic aspects of the Hitchin system for $\mathrm {GL}
_n $. Our results include the following.(a) We prove the motivic decomposition conjecture of …
_n $. Our results include the following.(a) We prove the motivic decomposition conjecture of …
Topological K-theory of quasi-BPS categories for Higgs bundles
T Pădurariu, Y Toda - arXiv preprint arXiv:2409.10800, 2024 - arxiv.org
In a previous paper, we introduced quasi-BPS categories for moduli stacks of semistable
Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the …
Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the …
Lie algebroid connections, twisted Higgs bundles and motives of moduli spaces
D Alfaya, A Oliveira - Journal of Geometry and Physics, 2024 - Elsevier
Abstract Let L=(L,[⋅,⋅], δ) be an algebraic Lie algebroid over a smooth projective curve X of
genus g≥ 2 such that L is a line bundle whose degree is less than 2− 2 g. Let r and d be …
genus g≥ 2 such that L is a line bundle whose degree is less than 2− 2 g. Let r and d be …
Complex K-theory of moduli spaces of Higgs bundles
M Groechenig, S Shen - arXiv preprint arXiv:2212.10695, 2022 - arxiv.org
We establish an isomorphism of complex $ K $-theory of the moduli space $\check {\mathcal
{M}} $ of $``SL_n" $-Higgs bundles of degree $ d $ and rank $ n $(in the sense of Hausel …
{M}} $ of $``SL_n" $-Higgs bundles of degree $ d $ and rank $ n $(in the sense of Hausel …