arXiv · math/9911044
The connection between these Fano 3-folds and plane quartic curves is explained.
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Frank-Olaf Schreyer. 1999-11-08. Geometry and Algebra of prime Fano 3-folds of genus 12. https://arxiv.org/abs/math/9911044
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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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