arXiv · 2007.14207
This paper is a survey about cylinders in Fano varieties and related problems.
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Ivan Cheltsov, Jihun Park, Yuri Prokhorov, Mikhail Zaidenberg. 2021-05-09. Cylinders in Fano varieties. https://arxiv.org/abs/2007.14207
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We prove that smooth Fano 3-folds in the families 2.18 and 3.4 are K-stable.
The G3-property of a subvariety was introduced by Hironaka-Matsumura, and plays an important role for deducing connectedness and extension results. Unfortunately, it's a rather elusive notion, which is not always easy to establish. Most of the existing work is concentrated on subvarieties of homogeneous varieties. The first goal of this article is to show that mobility assumptions on the subvariety, considered in works of Badescu, Chow, Debarre, Voisin, yield a certain partial positivity property, slightly stronger than G3, previously introduced by the author. Second, we apply the result to prove that, in numerous situations, the splitting of the normal bundle of a smooth two-codimensional subvariety implies that it is a complete intersection.
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