On the Cox ring of blowing up the diagonal

Abstract

We compute the Cox rings of the blow-ups ${\mathrm{Bl}}_{\Delta }(X^{\prime }\times X^{\prime })$ and ${\mathrm{Bl}}_{\Delta }({\mathbb{P}}_1^n)$ where $X^{\prime }$ is a product of projective spaces and $\Delta$ is the (generalised) diagonal.

8 pages

References in corpus (1)

• ${\overline{M}}_{0,n}$ is not a Mori Dream Space

Cited by in corpus (2)

• Cox rings of cubic surfaces and Fano threefolds
• Point Configurations and Translations