Equivariant compactifications of vector groups with high index

TL;DR

This paper classifies certain smooth Fano manifolds that serve as equivariant compactifications of vector groups, focusing on those with a high index relative to their dimension.

Contribution

It provides a classification of smooth equivariant compactifications of vector groups with high index, expanding understanding of their geometric structure.

Findings

Classified all such compactifications with index ≥ n-2.

Identified specific geometric properties of these manifolds.

Extended the theory of equivariant compactifications in algebraic geometry.

Abstract

In this note, we classify smooth equivariant compactifications of $\mathbb{G}_a^n$ which are Fano manifolds with index $\geq n-2$.