# zbMATH — the first resource for mathematics

Singularities of pluri-theta divisors in $$\mathrm{char} p>0$$. (English) Zbl 1360.14112
Chen, Jungkai Alfred (ed.) et al., Algebraic geometry in East Asia – Taipei 2011. Proceedings of the conference, Taipei, Taiwan, November 16–20, 2011. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-024-2). Advanced Studies in Pure Mathematics 65, 117-122 (2015).
Summary: 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 $$\mathrm{ mult}_x(D)\leq m\cdot \dim X$$ for any $$x\in X$$.
For the entire collection see [Zbl 1321.14003].

##### MSC:
 14K05 Algebraic theory of abelian varieties 14F17 Vanishing theorems in algebraic geometry 13A35 Characteristic $$p$$ methods (Frobenius endomorphism) and reduction to characteristic $$p$$; tight closure
Full Text: