Seshadri Constants and Interpolation on Commutative Algebraic Groups

TL;DR

This paper improves interpolation estimates on certain compactifications of commutative algebraic groups by leveraging Seshadri constants and vanishing theorems, achieving results comparable to the best known multiplicity estimates.

Contribution

It introduces a novel approach using Seshadri constants and properties of Serre's compactifications to significantly enhance interpolation estimates.

Findings

Quantitative improvement over previous estimates

Results match the accuracy of leading multiplicity estimates

Utilizes special properties of algebraic group compactifications

Abstract

In this article we study interpolation estimates on a special class of compactifications of commutative algebraic groups constructed by Serre. We obtain a large quantitative improvement over previous results due to Masser and the first author and our main result has the same level of accuracy as the best known multiplicity estimates. The improvements come both from using special properties of the compactifications which we consider and from a different approach based upon Seshadri constants and vanishing theorems.