3 citations · 6 across the 13 of their papers we have counts for
13 papers
A Matsushima theorem for K-polystable polarised smooth Fano threefolds
Hamid Abban, Paolo Cascini, Ivan Cheltsov
We prove that if is a smooth Fano threefold and is an ample -divisor such that is K-polystable, then the automorphism group is r…
On K-stability of singular hyperelliptic Fano 3-folds
Hamid Abban, Ivan Cheltsov, Adrien Dubouloz +3
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.
Smooth Fano 3-folds satisfying Condition (A)
Hamid Abban, Ivan Cheltsov, Takashi Kishimoto +1
A smooth variety is said to satisfy Condition (A) if every finite abelian subgroup of its automorphism group has a fixed point. We classify smooth Fano 3-folds that satisfy Conditi…
K-stability of Fano 3-folds in the World of Null-A
Hamid Abban, Ivan Cheltsov, Takashi Kishimoto +1
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…
K-stability of pointless del Pezzo surfaces and Fano 3-folds
Hamid Abban, Ivan Cheltsov, Takashi Kishimoto +1
We explore connections between existence of -rational points for Fano varieties defined over , a subfield of , and existence of Kähler-Einstein metrics on…
One-dimensional components in the K-moduli of smooth Fano 3-folds
Hamid Abban, Ivan Cheltsov, Elena Denisova +5
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…
On K-moduli of quartic threefolds
Hamid Abban, Ivan Cheltsov, Alexander Kasprzyk +2
The family of smooth Fano 3-folds with Picard rank 1 and anticanonical volume 4 consists of quartic 3-folds and of double covers of the 3-dimensional quadric branched along an octi…
Seshadri constants and K-stability of Fano manifolds
Hamid Abban, Ziquan Zhuang
We give a lower bound of the -invariants of ample line bundles in terms of Seshadri constants. As applications, we prove the uniform K-stability of infinitely many families of F…
K-stability of Fano varieties via admissible flags
Hamid Abban, Ziquan Zhuang
We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces…
Stability of fibrations over one-dimensional bases
Hamid Abban, Maksym Fedorchuk, Igor Krylov
We introduce and study a new notion of stability for varieties fibered over curves, motivated by Kollár's stability for homogeneous polynomials with integral coefficients. We devel…
Double Veronese cones with 28 nodes
Hamid Abban, Ivan Cheltsov, Jihun Park +1
We study nodal del Pezzo 3-folds of degree (also known as double Veronese cones) with singularities, which is the maximal possible number of singularities for such varieti…
Birational rigidity of orbifold degree 2 del Pezzo fibrations
Hamid Abban, Igor Krylov
Varieties fibered into del Pezzo surfaces form a class of possible outputs of the minimal model program. It is known that del Pezzo fibrations of degrees and over the proje…
Circle of Sarkisov links on a Fano -fold
Hamid Abban, Francesco Zucconi
For a general Fano -fold of index in the weighted projective space we construct new birational models that are Mori fibre spaces, in the fram…