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arXiv · 1404.0909

Deforming elephants of Q-Fano threefolds

Taro Sano
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Abstract

We study deformations of a pair of a $\mathbb{Q}$-Fano $3$-fold $X$ with only terminal singularities and its elephant $D \in |{-}K_X|$. We prove that, if there exists $D \in |{-}K_X|$ with only isolated singularities, the pair $(X,D)$ can be deformed to a pair of a $\mathbb{Q}$-Fano $3$-fold with only quotient singularities and a Du Val elephant. When there are only non-normal elephants, we reduce the existence problem of such a deformation to a local problem around the singular locus of the elephant. We also give several examples of $\mathbb{Q}$-Fano $3$-folds without Du Val elephants.

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Taro Sano. 2014-04-03. Deforming elephants of Q-Fano threefolds. https://arxiv.org/abs/1404.0909

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