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arXiv · 1302.3691

Cohomology bounds for sheaves of dimension one

Jinwon Choi·Kiryong Chung
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Abstract

We find the sharp bounds on $h^0(F)$ for one-dimensional semistable sheaves $F$ on a projective variety $X$ by using the spectrum of semistable sheaves. The result generalizes the Clifford theorem. When $X$ is the projective plane $\mathbb{P}^2$, we study the stratification of the moduli space by the spectrum of sheaves. We show that the deepest stratum is isomorphic to a subscheme of a relative Hilbert scheme. This provides an example of a family of semistable sheaves having the biggest dimensional global section space.

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Jinwon Choi, Kiryong Chung. 2013-05-05. Cohomology bounds for sheaves of dimension one. https://doi.org/10.1142/s0129167x14501031

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