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arXiv · 2002.04360

Multiplicities of irreducible theta divisors

Victor Lozovanu
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Abstract

Let $(A,\Theta)$ be a complex principally polarized abelian variety of dimension $g\geq 4$. Based on vanishing theorems, differentiation techniques and intersection theory, we show that whenever the theta divisor $\Theta$ is irreducible, its multiplicity at any point is at most $g-2$. This improves work of Koll\'ar, Smith-Varley, and Ein-Lazarsfeld. We also introduce some new ideas to study the same type of questions for pluri-theta divisors.

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Victor Lozovanu. 2020-02-11. Multiplicities of irreducible theta divisors. https://arxiv.org/abs/2002.04360

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