Euler characteristics of moduli of twisted sheaves on Enriques surfaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929735547748352 |
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| author | van Bree, Dirk Wang, Weisheng |
| author_facet | van Bree, Dirk Wang, Weisheng |
| contents | Let $Y$ be an Enriques surface and let $\mathcal{A}$ be an Azumaya algebra corresponding to the non-trivial Brauer class. Let $M$ be the moduli space of stable twisted sheaves on Enriques surfaces with twisted Chern character $M^H_{\mathcal{A}/Y}(2,c_1,\operatorname{ch}_2)$ with virtual dimension $N$. We show that the virtual Euler characteristic $e^\mathrm{vir}(M)$ only depends on $N$, more precisely, $e^\mathrm{vir}(M)=0$ when $N$ is odd and $e^\mathrm{vir}(M)=2\cdot e(Y^{[\frac{N}{2}]})$ when $N$ is even. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Euler characteristics of moduli of twisted sheaves on Enriques surfaces van Bree, Dirk Wang, Weisheng Algebraic Geometry Let $Y$ be an Enriques surface and let $\mathcal{A}$ be an Azumaya algebra corresponding to the non-trivial Brauer class. Let $M$ be the moduli space of stable twisted sheaves on Enriques surfaces with twisted Chern character $M^H_{\mathcal{A}/Y}(2,c_1,\operatorname{ch}_2)$ with virtual dimension $N$. We show that the virtual Euler characteristic $e^\mathrm{vir}(M)$ only depends on $N$, more precisely, $e^\mathrm{vir}(M)=0$ when $N$ is odd and $e^\mathrm{vir}(M)=2\cdot e(Y^{[\frac{N}{2}]})$ when $N$ is even. |
| title | Euler characteristics of moduli of twisted sheaves on Enriques surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2502.21073 |