Cohomological $\chi $ -dependence of ring structure for the moduli of one-dimensional sheaves on $\mathbb {P}^2$
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 characteristics. This stands in contrast to the $\chi $ -independence of the Betti numbers of these modul...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2024-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424000318/type/journal_article |
| Summary: | 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 characteristics. This stands in contrast to the
$\chi $
-independence of the Betti numbers of these moduli spaces. As a corollary, we deduce that
$M_{d,\chi }$
are topologically different unless they are related by obvious symmetries, strengthening a previous result of Woolf distinguishing them as algebraic varieties. |
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| ISSN: | 2050-5094 |