Schubert varieties are log Fano over the integers

TL;DR

This paper proves that Schubert varieties can be equipped with a divisor over the integers to form log Fano pairs in all characteristics, advancing understanding of their geometric properties.

Contribution

It introduces a divisor over the integers making Schubert varieties log Fano in all characteristics, a novel uniform approach in algebraic geometry.

Findings

Schubert varieties admit a divisor over the integers making them log Fano in all characteristics.

The pair (X_w, Δ) is log Fano universally across characteristics.

The result applies to all Schubert varieties, providing a new perspective on their positivity properties.

Abstract

Given a Schubert variety X_w, we exhibit a divisor \Delta, defined over the integers, such that the pair (X_w,\Delta) is log Fano in all characteristics.