Lower bounds for Seshadri constants via successive minima of line bundles

François Ballaÿ (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

Given a nef and big line bundle L on a projective variety of dimension d ≥ 2, we prove that the Seshadri constant of L at a very general point is larger than (d + 1)^{1/d −1}. This slightly improves the lower bound 1/d established by Ein, Küchle and Lazarsfeld. The proof relies on the concept of successive minima for line bundles recently introduced by Ambro and Ito.

Domaines: Géométrie algébrique [math.AG]

François Ballaÿ. Lower bounds for Seshadri constants via successive minima of line bundles. 2022. ⟨hal-03606565v2⟩