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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].

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
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