Sur une in\'egalit\'e fonctionnelle sur les vari\'et\'es toriques avec application \`a la torsion analytique holomorphe

TL;DR

This paper introduces a new functional on metrics over line bundles on complex toric varieties, compares it to classical functionals, and studies its impact on holomorphic analytic torsion variation.

Contribution

It defines a novel functional $V_ abla$ on invariant metrics on line bundles over toric varieties and analyzes its relation to existing functionals and torsion.

Findings

The functional $V_ abla$ is comparable to classical functionals.

The variation of holomorphic analytic torsion is studied using the new functional.

Results provide insights into metric behavior on toric varieties.

Abstract

Let $X$ be a complex non-singular toric variety, $E$ an equivariant and ample line bundle on $X$. We introduce a new functional $V_\infty$ on the set of smooth, positive and invariant metrics on $E$. We compare $V_\infty$ to some classical functionals. As an application, we study the variation of the holomorphic analytic torsion.