相关论文: K-stable Fano threefolds of rank 2 and degree 30
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 prove that smooth Fano 3-folds in the families 2.18 and 3.4 are K-stable.
We prove that all smooth Fano threefolds of rank 4 and degree 24 are K-stable.
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 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 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 find all K-polystable limits of smooth Fano threefolds in family 3.10.
We prove K-stability of smooth Fano 3-folds of Picard rank 3 and degree 22 that satisfy very explicit generality condition.
We show that there exists a K-stable smooth Fano threefold of the Picard rank 3, the anti-canonical degree 28 and the third Betti number 2.
We prove K-stability of smooth Fano 3-folds of Picard rank 3 and degree 20 that satisfy very explicit generality condition.
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…
We describe the automorphism groups of smooth Fano threefolds of rank 2 and degree 28 in the cases where they are finite.
We classify Q-Fano threefolds of Fano index > 2 and big degree.
We show that general one-nodal prime Fano threefolds of genus $12$ are K-polystable.
We study Fano threefolds that can be obtained by blowing up the three-dimensional projective space along a smooth curve of degree six and genus three. We produce many new K-stable examples of such threefolds, and we describe all finite…
By identifying K-polystable limits in 4 specific deformations families of smooth Fano 3-folds, we complete the classification of one-dimensional components in the K-moduli space of smoothable Fano 3-folds.
We prove the $K$-polystability of all smooth complex Fano threefolds admitting an effective action of $\text{SL}_2$ but not of a 2-torus or 3-torus. In particular, the existence of K\"{a}hler-Einstein metrics on varieties in the families…
A variety is said to satisfy Condition (A) if every finite abelian subgroup of its automorphism group has a fixed point. We show that a smooth Fano 3-fold not satisfying Condition (A) is K-polystable unless it is contained in eight…
We provide examples of smooth three-dimensional Fano complete intersections of dergee 2, 4, 6, and 8 that have coregularity 0. Considering the main theorem of arXiv:2309.16784 on the remaining 101 families of smooth Fano threefolds, our…
Based on the former parts, we classify smooth Fano threefolds of positive characteristic.