Stability of Frobenius direct images over surfaces

Congjun Liu; Mingshuo Zhou

Stability of Frobenius direct images over surfaces

Algebraic Geometry 2014-07-28 v1

Authors: Congjun Liu , Mingshuo Zhou

Abstract

Let $X$ be a smooth projective surface over an algebraically closed field $k$ of characteristic $p> 0$ with $\Omega_{X}^{1}$ semistable and $\mu(\Omega_{X}^{1})>0$ . For any semistable (resp. stable) bundle $W$ of rank $r$ , we prove that $F_*W$ is semistable (resp. stable) when $p\geq r(r-1)^2+1$ .

Keywords

Frobenius direct image semistable bundle smooth projective surface positive characteristic slope stability

Cite

@article{arxiv.1407.6899,
  title  = {Stability of Frobenius direct images over surfaces},
  author = {Congjun Liu and Mingshuo Zhou},
  journal= {arXiv preprint arXiv:1407.6899},
  year   = {2014}
}

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10 pages

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