Morgan V. Brown
Published 2011-09-28, updated 2012-02-17Version 2
Let $X$ be a smooth complete Fano variety over $\mathbb{C}$. We show that the Cox ring $\bigoplus_{L\in\text{Pic}(X)}H^0(X,\mathcal{O}_X(L))$ is Gorenstein with canonical singularities.
Comments: 15 pages, 2 tikz figures. Added log Fano and log Calabi-Yau cases, and included an example of a non Cohen-Macaulay Cox ring due to Yoshinori Gongyo
Cox ring of the generic fiber
The Cox ring of an algebraic variety with torus action
The canonical module of a Cox ring
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