Related papers: A characterization of Fano type varieties

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

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

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

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…

We give a necessary and sufficient condition for a generalized Bott manifold to be Fano or weak Fano. As a consequence we characterize Fano Bott manifolds.

We prove a result on the existence of linear forms of a given Diophantine type.

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

This paper is a survey about cylinders in Fano varieties and related problems.

We give examples of Fano varieties $X$ with Picard number 1, which have terminal singularities and admit endomorphisms with degree larger than 1.

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…

In this paper, we study the structure of Fano fibrations of varieties admitting an int-amplified endomorphism. We prove that if a normal $\mathbb{Q}$-factorial klt projective variety $X$ has an int-amplified endomorphism, then there exists…

For Fano varieties of various singularities such as canonical and terminal, we construct examples with large Fano index. By low-dimensional evidence, we conjecture that our examples have the largest Fano index for all dimensions.

Based on the former parts, we classify smooth Fano threefolds of positive characteristic.

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

We prove divisorial canonicity of Fano hypersurfaces and double spaces of general position with elementary singularities.

We give a simple necessary and sufficient condition for uniform K-stability of $\mathbb{Q}$-Fano varieties.

We classify three-dimensional Fano varieties with canonical Gorenstein singularities of degree bigger than 64.

We prove that a projective surface of globally $F$-regular type defined over a field of characteristic zero is of Fano type.

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.