Angehrn-Siu-Helmke's method applied to abelian varieties

Zhi Jiang

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arXiv · 2207.04627

Angehrn-Siu-Helmke's method applied to abelian varieties

Zhi Jiang

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Abstract

We apply Angehrn-Siu-Helmke's method to estimate basepoint freeness thresholds of higher dimensional polarized abelian varieties. We showed that a conjecture of Caucci holds for very general polarized abelian varieties in the moduli spaces $\mathcal A_{g, l}$ with only finitely many possible exceptions of polarization types $l$ in each dimension $g$. We improved the bound of basepoint freeness thresholds of any polarized ableian $4$-folds and simple abelian $5$-folds.

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Zhi Jiang. 2022-07-11. Angehrn-Siu-Helmke's method applied to abelian varieties. https://arxiv.org/abs/2207.04627

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