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arXiv · 2010.08897

Frobenius stable pluricanonical systems on threefolds of general type in positive characteristic

Lei Zhang
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Abstract

This paper aims to investigate effectivity problems of pluricanonical systems on varieties of general type in positive characteristic. In practice, we will consider a sub-linear system $|S^0_{-}(X, K_X + nK_X)| \subseteq |H^0(X, K_X +nK_X)|$ generated by certain Frobenius stable sections, and prove that for a minimal terminal threefold $X$ of general type with either $q(X)>0$ or Gorenstein singularities, if $n\geq 28$ then $|S^0_{-}(X, K_X + nK_X)| \neq \emptyset$; if $n\geq 42$ then the linear system $|S^0_{-}(X, K_X + nK_X)|$ defines a birational map.

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Lei Zhang. 2020-10-18. Frobenius stable pluricanonical systems on threefolds of general type in positive characteristic. https://doi.org/10.1007/s11040-020-09363-1

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