相关论文: K-stability and space sextic curves of genus three

In this note, we study K-stability of smooth Fano threefolds that can be obtained by blowing up the three-dimensional projective space along a smooth elliptic curve of degree five.

We find all K-polystable smooth Fano threefolds that can be obtained as blowup of projective space along the disjoint union of a twisted cubic curve and a line.

We study K-stability of smooth Fano threefolds of Picard rank $2$ and degree $22$ which can be obtained by blowing up a smooth complete intersection of two quadrics in $\mathbb{P}^5$ along a conic. We also describe the automorphism groups…

In this article, we study the K-moduli space of Fano threefolds obtained by blowing up $\mathbb{P}^3$ along $(2,3)$-complete intersection curves. This K-moduli space is a two-step birational modification of the GIT moduli space of…

We prove that every smooth Fano threefold from the family No 2.8 is K-stable. Such a Fano threefold is a double cover of the blow-up of $\mathbb{P}^3$ at one point branched along an anti-canonical divisor.

We prove that all general smooth Fano threefolds of Picard rank $3$ and degree $14$ are K-stable, where the generality condition is stated explicitly.

We show that general one-nodal prime Fano threefolds of genus $12$ are K-polystable.

We prove that all smooth Fano threefolds with Picard rank 2 and degree 28 are K-polystable, except for some explicit cases which we describe. We also give a classification of the normal bundle of a rational normal quartic curve in a smooth…

We show that certain Galois covers of K-semistable Fano varieties are K-stable. We use this to give some new examples of Fano manifolds admitting K\"ahler-Einstein metrics, including hypersurfaces, double solids and threefolds.

We prove that all smooth Fano threefolds of rank 4 and degree 24 are K-stable.

Ross and Thomas introduced the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature K\"ahler metric. This paper presents a study of slope stability of Fano manifolds…

We prove that smooth Fano 3-folds in the families 2.18 and 3.4 are K-stable.

We prove K-stability of smooth Fano 3-folds of Picard rank 3 and degree 22 that satisfy very explicit generality condition.

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…

We prove K-stability of smooth Fano 3-folds of Picard rank 3 and degree 20 that satisfy very explicit generality condition.

We find all K-stable smooth Fano threefolds in the family No. 2.22.

We prove that all smooth Fano threefolds in the families 2.1, 2.2, 2.3, 2.4, 2.6 and 2.7 are K-stable, and we also prove that smooth Fano threefolds in the family 2.5 that satisfy one very explicit generality condition are K-stable.

We study the K-stability of singular Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system is base-point-free but not very ample.

We give new proofs of the K-polystability of two smooth Fano threefolds. One of them is a~smooth divisor in $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^2$ of degree $(1,1,1)$, which is unique up to isomorphism. Another one is the~blow…

We show that a Fano manifold (X,-K_X) is not slope stable with respect to a smooth curve Z if and only if (X,Z) is isomorphic to one of (projective space, line), (product of projective line and projective space, fiber of second projection)…