Cohomological $\chi$-dependence of ring structure for the moduli of one-dimensional sheaves on $\mathbb{P}^2$

Woonam Lim; Miguel Moreira; Weite Pi

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arXiv · 2305.14193

Cohomological $\chi$-dependence of ring structure for the moduli of one-dimensional sheaves on $\mathbb{P}^2$

Woonam Lim·Miguel Moreira·Weite Pi

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Abstract

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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BibTeX RIS

Woonam Lim, Miguel Moreira, Weite Pi. 2023-05-23. Cohomological $\chi$-dependence of ring structure for the moduli of one-dimensional sheaves on $\mathbb{P}^2$. https://arxiv.org/abs/2305.14193

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