Multiplicities of irreducible theta divisors

Abstract

Let $(A,\Theta )$ be a complex principally polarized abelian variety of dimension $g\ge 4$. 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 Kollár, Smith-Varley, and Ein-Lazarsfeld. We also introduce some new ideas to study the same type of questions for pluri-theta divisors.

23 pages. Improved exposition. Comments are welcome

References in corpus (2)

• Singular divisors and syzygies of polarized abelian threefolds
• Vanishing theorems and the multigraded regularity of nonsingular subvarieties