Multiprojective Seshadri stratifications and Young-tableaux

TL;DR

This paper introduces a geometric interpretation of Young-tableaux using Seshadri stratifications, generalizing to multiprojective varieties to connect combinatorics with algebraic geometry.

Contribution

It extends Seshadri stratifications to multiprojective varieties and links Young-tableaux to vanishing multiplicities on Schubert varieties.

Findings

Established a new algebraic-geometric framework for Young-tableaux.

Generalized Seshadri stratifications to multiprojective varieties.

Connected combinatorial columns to geometric vanishing multiplicities.

Abstract

We provide an algebraic-geometrical interpretation of the classical semistandard Young-tableaux via the notion of Seshadri stratifications. The columns appearing in such a tableau correspond to vanishing multiplicities of certain rational functions on Schubert varieties. To build a framework for this correspondence we generalize Seshadri stratifications to multiprojective varieties, which forms the largest part of this article.