cox_rings.md

CurrentModule = Oscar

Cox rings

Cox rings of linear quotients

By a theorem of Arzhantsev and Gaifullin AG10, the Cox ring of a linear quotient $V/G$ is graded isomorphic to the invariant ring $K[V]^{[G,G]}$, where $[G,G]$ is the derived subgroup of $G$.

cox_ring(L::LinearQuotient)

Cox rings of $\mathbb Q$-factorial terminalizations

We provide an experimental algorithm to compute the Cox ring of a $\mathbb Q$-factorial terminalization $X\to V/G$ of a linear quotient due to Yam18.

cox_ring_of_qq_factorial_terminalization(L::LinearQuotient)