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 …

Holomorphic anomaly equation for

P Bousseau, H Fan, S Guo, L Wu - Forum of Mathematics, Pi, 2021 - cambridge.org
Holomorphic anomaly equation for (P2 , ) and the Nekrasov-Shatashvili limit of local P Page 1
Forum of Mathematics, Pi (2021), Vol. 9:e3 1–57 doi:10.1017/fmp.2021.3 RESEARCH ARTICLE …

Perverse filtrations, Chern filtrations, and refined BPS invariants for local P2

Y Kononov, W Pi, J Shen - Advances in Mathematics, 2023 - Elsevier
We explore connections between three structures associated with the cohomology of the
moduli of 1-dimensional stable sheaves on P 2: perverse filtrations, tautological classes, and …

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 …

[PDF][PDF] Cohomological stabilization, perverse filtrations, and refined BPS invariants for del Pezzo surfaces

W Pi, J Shen, F Si, F Zhang - arXiv preprint arXiv …, 2024 - changfeng1992.github.io
We prove an asymptotic product formula for the refined BPS invariants associated with a
local del Pezzo surface. Our formula governs the cohomological stabilization of the perverse …

Some Betti numbers of the moduli of 1-dimensional sheaves on ℙ2

Y Yuan - Forum Mathematicum, 2024 - degruyter.com
Let M⁢(d, χ), with (d, χ)= 1, be the moduli space of semistable sheaves on ℙ 2 supported on
curves of degree d and with Euler characteristic χ. The cohomology ring H*⁢(M⁢(d, χ), ℤ) of …

Holomorphic Floer theory and Donaldson-Thomas invariants

P Bousseau - String-Math 2022, 2024 - books.google.com
We present several expected properties of the holomorphic Floer theory of a holomorphic
symplectic manifold. In particular, we propose a conjecture relating holomorphic Floer theory …

Quivers and curves in higher dimension

H Argüz, P Bousseau - Transactions of the American Mathematical Society, 2025 - ams.org
We prove a correspondence between Donaldson–Thomas invariants of quivers with
potential having trivial attractor invariants and genus zero punctured Gromov–Witten …

On the complex affine structures of SYZ fibration of Del Pezzo surfaces

SC Lau, TJ Lee, YS Lin - arXiv preprint arXiv:2005.04825, 2020 - arxiv.org
Given any smooth cubic curve $ E\subseteq\mathbb {P}^ 2$, we show that the complex
affine structure of the special Lagrangian fibration of $\mathbb {P}^ 2\setminus E …

BPS invariants of symplectic log Calabi-Yau fourfolds

M Farajzadeh-Tehrani - Transactions of the American Mathematical Society, 2024 - ams.org
Using the Fredholm setup of Farajzadeh-Tehrani [Peking Math. J.(2023), https://doi.
org/10.1007/s42543-023-00069-1], we study genus zero (and higher) relative Gromov …