A lower bound on Seshadri constants of hyperplane bundles on threefolds

TL;DR

This paper establishes a lower bound for Seshadri constants of very ample line bundles on threefolds, extending Bauer's theorem to singular surfaces and applying it to smooth threefolds.

Contribution

It provides a new lower bound for Seshadri constants on threefolds and generalizes Bauer's theorem to singular surfaces.

Findings

Lower bound for Seshadri constants on threefolds established

Extension of Bauer's theorem to singular surfaces

Application to smooth threefolds with improved bounds

Abstract

We give the lower bound on Seshadri constants for the case of very ample line bundles on threefolds. We consider the situation when the Seshadri constant is strictly less than 2 and give a version of Bauer's theorem \cite[Theorem 2.1]{B1} for singular surfaces so we can prove the same result for smooth threefolds.