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 …

Cohomological -independence for Higgs bundles and Gopakumar–Vafa invariants

T Kinjo, N Koseki - Journal of the European Mathematical Society, 2024 - ems.press
The aim of this paper is two-fold. Firstly, we prove Toda's-independence conjecture for
Gopakumar–Vafa invariants of arbitrary local curves. Secondly, following Davison's work, we …

Generators for the cohomology ring of the moduli of one-dimensional sheaves on

W Pi, J Shen - arXiv preprint arXiv:2204.05866, 2022 - arxiv.org
We explore the structure of the cohomology ring of the moduli space of stable 1-dimensional
sheaves on $\mathbb {P}^ 2$ of any degree. We obtain a minimal set of tautological …

Nonabelian Hodge isomorphisms for stacks and cohomological Hall algebras

L Hennecart - arXiv preprint arXiv:2307.09920, 2023 - arxiv.org
In this paper, we complete the nonabelian Hodge theory triangle of isomorphisms for stacks
between the Borel-Moore homologies of the Dolbeault, Betti and de Rham moduli stacks …

Hodge-to-singular correspondence for reduced curves

M Mauri, L Migliorini - Journal of the European Mathematical Society, 2024 - ems.press
We study the summands of the decomposition theorem for the Hitchin system for GLn, in
arbitrary degree, over the locus of reduced spectral curves. A key ingredient is a new …

A cohomological non abelian Hodge theorem in positive characteristic

MAA de Cataldo, S Zhang - arXiv preprint arXiv:2104.12970, 2021 - arxiv.org
We start with a curve over an algebraically closed ground field of positive characteristic $ p>
0$. By using specialization techniques, under suitable natural coprimality conditions, we …

Combinatorial decomposition theorem for Hitchin systems via zonotopes

M Mauri, L Migliorini, R Pagaria - arXiv preprint arXiv:2209.00621, 2022 - arxiv.org
arXiv:2209.00621v2 [math.AG] 6 Jul 2023 Page 1 COMBINATORIAL DECOMPOSITION
THEOREM FOR HITCHIN SYSTEMS VIA ZONOTOPES MIRKO MAURI, LUCA MIGLIORINI AND …

Cohomological

W Lim, M Moreira, W Pi - Forum of Mathematics, Sigma, 2024 - cambridge.org
Cohomological 𝝌-dependence of ring structure for the moduli of one-dimensional sheaves
on P2 Page 1 Forum of Mathematics, Sigma (2024), Vol. 12:e47 1–17 doi:10.1017/fms.2024.31 …

Cohomological -dependence of ring structure for the moduli of one-dimensional sheaves on

W Lim, M Moreira, W Pi - arXiv preprint arXiv:2305.14193, 2023 - arxiv.org
We prove that the cohomology rings of the moduli space $ M_ {d,\chi} $ of one-dimensional
sheaves on the projective plane are not isomorphic for general different choices of the Euler …

[引用][C] Cohomological χ-dependence of ring structure for the moduli of one-dimensional sheaves on P 2

W Lim, M Moreira, W Pi - arXiv preprint arXiv:2305.14193, 2023