Equivariant completions of affine spaces

Ivan Arzhantsev, Yulia Zaitseva

Published 2020-08-22Version 1

We survey recent results on open embeddings of the affine space $\mathbb{C}^n$ into a complete algebraic variety $X$ such that the action of the vector group $\mathbb{G}_a^n$ on $\mathbb{C}^n$ by translations extends to an action of $\mathbb{G}_a^n$ on $X$. The current version of the text includes the introduction and the section on equivariant embeddings into the projective space $\mathbb{P}^n$. Comments and suggestions are very welcome.