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arXiv · 0905.2011

Stability of sheaves of locally closed and exact forms

Xiaotao Sun
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Abstract

For any smooth projective variety $X$ of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$ with $μ(Ω^1_X)>0$. If ${\rm T}^{\ell}(Ω^1_X)$ ($0<\ell 0$ and $Ω^1_X$ is semi-stable, the sheaf $B^2_X$ of exact 2-forms is also stable. Moreover, under the same condition, the sheaf $Z^1_X$ of closed 1-forms is stable when $p>3$, and $Z^1_X$ is semi-stable when $p=3$.

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Xiaotao Sun. 2009-05-13. Stability of sheaves of locally closed and exact forms. https://arxiv.org/abs/0905.2011

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