Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Equivariant completions of toric varieties and their degenerations

Seminar | April 2 | 5-6 p.m. | 939 Evans Hall | Canceled

 Netanel Friedenberg, Yale University

 Department of Mathematics

I will tell the story of equivariant completion of toric varieties and their degenerations from the perspectives of algebraic geometry and combinatorics. We will start on the algebraic geometry side with results of Nagata and Sumihiro on completions of varieties. We will then move on to later combinatorial proofs that normal toric varieties admit completions. Finally, we will discuss recent results which show that certain degenerations of toric varieties admit equivariant completions. We will see that, in contrast to the earlier part of the story, the algebraic-geometric proof does not show the existence of normal equivariant completions, whereas the combinatorial proof does.