Related papers: Cylinders in Fano varieties

Cylinders in Fano varieties receives a lot of attentions recently from the viewpoints of birational geometry and unipotent geometry. In this article, we provide a survey of several known et new results concerning the anti-canonically polar…

In this note we collect some results on the deformation theory of toric Fano varieties.

We overview some recent results on Fano varieties giving evidence of their rigid nature under small deformations.

We prove a characterization of Fano type varieties.

In this note, we discuss a number of open problems in K-stability theory.

We give a characterization of Fano type surfaces with large cyclic automorphisms.

We investigate numerically Fano resonances excited in periodic arrays of dielectric, metallic and left-handed cylinders. Of particular interest are Fano resonances excited in the linear array of cylin- ders. We analyze spatial distribution…

Fano varieties are subvarieties of the Grassmannian whose points parametrize linear subspaces contained in a given projective variety. These expository notes give an account of results on Fano varieties of complete intersections, with a…

We list combinatorial criteria of some singularities, which appear in the Minimal Model Program or in the study of (singular) Fano varieties, for spherical varieties. Most of the results of this paper are already known or are quite easy…

We study a wide class of affine varieties, which we call affine Fano varieties. By analogy with birationally super-rigid Fano varieties, we define super-rigidity for affine Fano varieties, and provide many examples and non-examples of…

This note is about cycle-theoretic properties of the Fano variety of lines on a smooth cubic fivefold. The arguments are based on the fact that this Fano variety has finite-dimensional motive. We also present some results concerning Chow…

We prove that a weak Fano manifold has unobstructed deformations. For a general variety, we investigate conditions under which a variety is necessarily obstructed.

We investigate Fano varieties defined over a number field that contain subvarieties whose number of rational points of bounded height is comparable to the total number on the variety.

We investigate birational boundedness of Fano varieties and Fano fibrations. We establish an inductive step towards birational boundedness of Fano fibrations via conjectures related to boundedness of Fano varieties and Fano fibrations. As…

The aim of this note is to settle some foundational questions about the behavior of birational rigidity in extensions of algebraically closed fields.

This article gives an overview of toric Fano and toric weak Fano varieties associated to graphs and building sets. We also study some properties of such toric Fano varieties and discuss related topics.

This is a survey on the Fano schemes of linear spaces, conics, rational curves, and curves of higher genera in smooth projective hypersurfaces, complete intersections, Fano threefolds, etc.

We survey some results obtained in our quest for Fano varieties of K3 type and discuss why exploring the singular world might be interesting for discovering new K3 structures.

We study the anti-canonical ring of a projective variety and we characterise varieties of log Fano type depending on the singularities of these models.

We give a survey of the recent progress on the study of K-stability of Fano varieties by an algebro-geometric approach.