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arXiv · 1109.6368

Singularities of Cox Rings of Fano Varieties

Morgan V. Brown
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Abstract

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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Morgan V. Brown. 2012-02-17. Singularities of Cox Rings of Fano Varieties. https://arxiv.org/abs/1109.6368

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