Download this article
 Download this article For screen
For printing
Recent Issues

Volume 28
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
Cohomological $\chi$–independence for moduli of one-dimensional sheaves and moduli of Higgs bundles

Davesh Maulik and Junliang Shen

Geometry & Topology 27 (2023) 1539–1586

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 ample curve class on a toric del Pezzo surface is independent of the Euler characteristic of the sheaves. We also prove an analogous result for the moduli space of semistable Higgs bundles with respect to an effective divisor D of degree deg (D) > 2g 2. Our results confirm the cohomological χ–independence conjecture by Bousseau for 2, and verify Toda’s conjecture for Gopakumar–Vafa invariants for certain local curves and local surfaces.

For the proof, we combine a generalized version of Ngô’s support theorem, a dimension estimate for the stacky Hilbert–Chow morphism, and a splitting theorem for the morphism from the moduli stack to the good GIT quotient.

moduli of sheaves, perverse sheaves, support theorem, Gopakumar–Vafa invariants
Mathematical Subject Classification
Primary: 14H60, 14J60, 14N35
Secondary: 32S60
Received: 10 January 2021
Revised: 1 October 2021
Accepted: 3 November 2021
Published: 15 June 2023
Proposed: Dan Abramovich
Seconded: Gang Tian, Richard P Thomas
Davesh Maulik
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
Junliang Shen
Department of Mathematics
Yale University
New Haven, CT
United States

Open Access made possible by participating institutions via Subscribe to Open.