Singularities of pluri-theta divisors in Char $p>0$

Details Singularities of pluri-theta divisors in Char $p>0$ Singularities of pluri-theta divisors in Char $p>0$

2011-12-09

arxiv.org/abs/1112.2219v1

Mathematics

Algebraic Geometry

Scientific paper

We show that if $(X,\Theta)$ is a PPAV over an algebraically closed field of
characteristic $p>0$ and $D\in |m\Theta|$, then $(X,\frac 1 m D)$ is a limit of
strongly $F$-regular pairs and in particular ${\rm mult}_x(D)\leq m\cdot \dim
X$ for any $x\in X$.

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