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

Abstract

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 ${\mathrm{mult}}_x(D)\le m\cdot \dim X$ for any $x\in X$.

References in corpus (1)

• Regularity on abelian varieties III: relationship with Generic Vanishing and applications

Cited by in corpus (3)

• F-singularities in families
• Pluri-canonical maps of varieties of maximal Albanese dimension in positive characteristic
• Irreducible Theta Divisors of PPAV's are Strongly F-regular