arXiv · 1809.02705
We classify smooth Fano threefolds that admit degenerations to toric Fano threefolds with ordinary double points.
Explore connections, maps & timelines
Sergey Galkin. 2018-09-07. Small toric degenerations of Fano threefolds. https://arxiv.org/abs/1809.02705
Cite the original work for its findings. Save a collection to share your selection of sources.
KEEP EXPLORING
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.
We define a natural extension of a universal factorization algebra $\mathcal{A}$ to families of stable punctured curves, by integrating over all semistable modifications. We prove that the resulting sheaf of factorization homology satisfies a natural gluing formula, by tensoring over a certain derived associative algebra $\mathfrak{Z}_{\mathcal{A}}^0$, generalizing the Verlinde formula for gluing of conformal blocks.