Multiplicities of irreducible theta divisors
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...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
11.02.2020
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| Subjects | |
| Online Access | Get full text |
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| Summary: | 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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| DOI: | 10.48550/arxiv.2002.04360 |