Stability of sheaves of locally closed and exact forms

Abstract

For any smooth projective variety $X$ of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$ with $\mu ({\Omega }_X^1)>0$. If ${\mathrm{T}}^{\ell }({\Omega }_X^1)$ ($0<\ell <n(p-1)$) are semi-stable, then the sheaf $B_X^1$ of exact 1-forms is stable. When $X$ is a surface with $\mu ({\Omega }_X^1)>0$ and ${\Omega }_X^1$ is semi-stable, the sheaf $B_X^2$ of exact 2-forms is also stable. Moreover, under the same condition, the sheaf $Z_X^1$ of closed 1-forms is stable when $p>3$, and $Z_X^1$ is semi-stable when $p=3$.

References in corpus (1)

• Direct images of bundles under Frobenius morphisms