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arXiv · 2111.10071

Sheaves on non-reduced curves in a projective surface

Yao Yuan
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Abstract

Sheaves on non-reduced curves can appear in moduli space of 1-dimensional semistable sheaves over a surface, and moduli space of Higgs bundles as well. We estimate the dimension of the stack $\mathbf{M}_{X}(nC,\chi)$ of pure sheaves supported at the non-reduced curve $nC~(n\geq 2)$ with $C$ an integral curve on $X$. We prove that the Hilbert-Chow morphism $h_{L,\chi}:\mathcal{M}^H_X(L,\chi)\rightarrow |L|$ sending each semistable 1-dimensional sheaf to its support have all its fibers of the same dimension for $X$ Fano or with trivial canonical line bundle and $|L|$ contains integral curves.

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Yao Yuan. 2021-11-19. Sheaves on non-reduced curves in a projective surface. https://arxiv.org/abs/2111.10071

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