Singularities of Cox Rings of Fano Varieties

Details Singularities of Cox Rings of Fano Varieties Singularities of Cox Rings of Fano Varieties

2011-09-28

arxiv.org/abs/1109.6368v2

Mathematics

Algebraic Geometry

15 pages, 2 tikz figures. Added log Fano and log Calabi-Yau cases, and included an example of a non Cohen-Macaulay Cox ring du

Scientific paper

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.

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