Non-annulation effective et positivit\'e locale des fibr\'es en droites amples adjoints

TL;DR

This paper establishes positivity results for Seshadri constants on certain threefolds and Fano varieties, utilizing Kawamata's non-vanishing conjecture and adjunction theory to advance understanding of line bundle properties.

Contribution

It proves the non-vanishing conjecture in dimension three for high-volume line bundles and demonstrates Seshadri constants exceeding 1 on specific threefolds with nef anticanonical bundles.

Findings

Seshadri constants > 1 on certain threefolds

Non-vanishing conjecture proved in dimension 3 for high-volume line bundles

Application of Kawamata's subadjunction formula

Abstract

We prove that Seshadri constants of some ample divisors are bigger than 1 on smooth threefolds whose anticanonical bundle is nef or on Fano varieties of small coindice. The main tools are (some known cases of) the Kawamata's effective non-vanishing conjecture and the adjunction theory. We prove the non-vanishing conjecture in dimension 3 in the case of line bundles of "high" volume using Kawamata's subadjunction formula.