Seshadri constants and degrees of defining polynomials

TL;DR

This paper explores the relationship between Seshadri constants and the degrees of defining polynomials, specifically computing these constants for Fano varieties as complete intersections in rational homogeneous spaces.

Contribution

It provides explicit computations of Seshadri constants for Fano varieties in a new geometric context involving rational homogeneous spaces.

Findings

Computed Seshadri constants on Fano varieties

Established a relation between Seshadri constants and polynomial degrees

Extended understanding of positivity in algebraic geometry

Abstract

In this paper, we study a relation between Seshadri constants and degrees of defining polynomials. In particular, we compute the Seshadri constants on Fano varieties obtained as complete intersections in rational homogeneous spaces of Picard number one.