Year: 2024
Type: article
Abstract: Let $(A, \Delta)$ be a complex principally polarized abelian variety of dimension $g \geqslant 4$. Based on vanishing theorems, differentiation techniques and intersection theory, we show that whenever the theta divisor $\Delta$ is irreducible, its multiplicity at any point is at most $g-2$. This improves work of Kollár $\href{https://doi.org/10.1515/9781400864195}{[23]}$, Smith–Varley $\href{https://doi.org/ 10.1215/S0012-7094-96-08214-9}{[37]}$, and Ein–Lazarsfeld $\href{ https://www.jstor.org/stable/2152909}{[13]}$. We also introduce some new ideas to study the same type of questions for pluri-theta divisors.
Source: Journal of Differential Geometry
Author: Victor Lozovanu
Institutions: Leibniz University Hannover, University of Genoa
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403451367