相关论文: On deformations 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.

We present some applications of the deformation theory of toric Fano varieties to K-(semi/poly)stability of Fano varieties. First, we present two examples of K-polystable toric Fano 3-fold with obstructed deformations. In one case, the…

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 paper is devoted to the study of various aspects of deformations of log pairs, especially in connection to questions related to the invariance of singularities and log plurigenera. In particular, using recent results from the minimal…

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

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

We construct one-parameter complex analytic families whose special fibers are complete toric varieties. Under some assumptions, the general fibers of these families also become toric varieties and we can explicitly describe the…

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 survey some results on toric topology.

We completely classify toric weakened Fano 3-folds, that is, smooth toric weak Fano 3-folds which are not Fano but are deformed to smooth Fano 3-folds. There exist exactly 15 toric weakened Fano 3-folds up to isomorphisms.

We give a new, shorter computation of Frobenius push-forwards of line bundles on toric varieties.

We extend the Altmann--Mavlyutov construction of homogeneous deformations of affine toric varieties to the case of toric pairs $(X, \partial X)$, where $X$ is an affine or projective toric variety and $\partial X$ is its toric boundary. As…

In this paper, we obtain a complete classification of smooth toric Fano varieties equipped with extremal contractions which contract divisors to curves for any dimension. As an application, we obtain a complete classification of smooth…

In these notes we provide the foundation for the deformation theoretic parts of arXiv:0807.3753 and arXiv:math/0102005.

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

We classify smooth Fano threefolds that admit degenerations to toric Fano threefolds with ordinary double points.

An algebraic deformation theory of dialgebra morphisms is obtained.

In this paper, we give a tropical method for computing Gromov-Witten type invariants of Fano manifolds of special type. This method applies to those Fano manifolds which admit toric degenerations to toric Fano varieties with singularities…

We study the Farrell and Jones Warping Deformation.