Cohomological χ -dependence of ring structure for the moduli of one-dimensional sheaves on P<SUP>2</SUP>

W Lim; M Moreira; WT Pi

doi:10.1017/fms.2024.31

Cohomological χ -dependence of ring structure for the moduli of one-dimensional sheaves on P<SUP>2</SUP>

W Lim, M Moreira, WT Pi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We prove that the cohomology rings of the moduli space of one-dimensional sheaves on the projective plane are not isomorphic for general different choices of the Euler characteristics. This stands in contrast to the-independence of the Betti numbers of these moduli spaces. As a corollary, we deduce that are topologically different unless they are related by obvious symmetries, strengthening a previous result of Woolf distinguishing them as algebraic varieties.

Original language	English
Article number	e47
Number of pages	17
Journal	Forum of Mathematics, Sigma
Volume	12
DOIs	https://doi.org/10.1017/fms.2024.31
Publication status	Published - 1 Apr 2024

Bibliographical note

Publisher Copyright:
© The Author(s), 2024. Published by Cambridge University Press.

Funding

The first author is supported by the grant SNF-200020-182181. The second author is supported by ERC-2017-AdG-786580-MACI. The project received funding from the European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme (grant agreement 786580).

Funders	Funder number
European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme	786580
Not added	SNF-200020-182181
Not added	ERC-2017-AdG-786580-MAC

Keywords

14D20 14C15

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cohomological-dollarchi-dollar-dependence-of-ring-structure-for-the-moduli-of-one-dimensional-sheaves-on-dollarmathbb-p2dollarFinal published version, 306 KBLicence: CC BY

Cite this

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Cohomological χ -dependence of ring structure for the moduli of one-dimensional sheaves on P<SUP>2</SUP>

Abstract

Bibliographical note

Funding

Keywords

Access to Document

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