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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2305.14193 |
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| _version_ | 1866909126247841792 |
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| author | Lim, Woonam Moreira, Miguel Pi, Weite |
| author_facet | Lim, Woonam Moreira, Miguel Pi, Weite |
| contents | We prove that the cohomology rings of the moduli space $M_{d,χ}$ 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 $χ$-independence of the Betti numbers of these moduli spaces. As a corollary, we deduce that $M_{d,χ}$ are topologically different unless they are related by obvious symmetries, strengthening a previous result of Woolf distinguishing them as algebraic varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_14193 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cohomological $χ$-dependence of ring structure for the moduli of one-dimensional sheaves on $\mathbb{P}^2$ Lim, Woonam Moreira, Miguel Pi, Weite Algebraic Geometry We prove that the cohomology rings of the moduli space $M_{d,χ}$ 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 $χ$-independence of the Betti numbers of these moduli spaces. As a corollary, we deduce that $M_{d,χ}$ are topologically different unless they are related by obvious symmetries, strengthening a previous result of Woolf distinguishing them as algebraic varieties. |
| title | Cohomological $χ$-dependence of ring structure for the moduli of one-dimensional sheaves on $\mathbb{P}^2$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2305.14193 |