Related papers: Unstable polarized del Pezzo surfaces
We give a simple sufficient condition for K-stability of polarized del Pezzo surfaces and for the existence of a constant scalar curvature Kahler metric in the Kahler class corresponding to the polarization.
In an algebro-geometric way, we completely determine whether smooth del Pezzo surfaces are K-(semi)stable or not.
We present new constructions of Kaehler metrics with constant scalar curvature on complex surfaces, in particular on certain del Pezzo surfaces. Some higher dimensional examples are provided as well.
We prove the existence of singular del Pezzo surfaces that are neither K-semistable nor contain any anticanonical polar cylinder.
In this paper, we shall show that a polarized algebraic manifold is K-stable if the polarization class admits a Kaehler metric of constant scalar curvature. This generalizes the results of Chen-Tian, Donaldson and Stoppa. (Parts of the…
For an arbitrary ample divisor A in smooth del Pezzo surface S of degree 1, we verify the condition of the polarization (S,A) to be K-stable and it is a simple numerical condition.
We give examples of smooth surfaces with negative first Chern class which are slope unstable with respect to certain polarisations, and so have Kahler classes that do not admit any constant scalar curvature Kahler metrics. We also compare…
We give examples of K-unstable singular del Pezzo surfaces which are weighted hypersurfaces with index 2.
We express notions of K-stability of polarized spherical varieties in terms of combinatorial data, vastly generalizing the case of toric varieties. We then provide a combinatorial sufficient condition of G-uniform K-stability by studying…
This article is concerned with an observation for proving non-existence of canonical Kahler metrics. The idea is to use a rather explicit type of degeneration that applies in many situations. Namely, in a variation on a theme introduced by…
We study the K-stability of a polarised variety with non-reductive automorphism group. We associate a canonical filtration of the co-ordinate ring to each variety of this kind, which destabilises the variety in several examples which we…
Motivated by the problem for the existence of K\"ahler-Einstein edge metrics, Cheltsov and Rubinstein conjectured the K-polystability of asymptotically log Fano varieties with small cone angles when the anti-log-canonical divisors are not…
In this short note, we study the asymptotic Chow polystability of toric Del Pezzo surfaces appear in the moduli space of K\"ahler-Einstein Fano varieties constructed in [OSS16].
We describe a notion of lattice polarization for rational elliptic surfaces and weak del Pezzo surfaces, and describe the complex moduli of the former and the K\"{a}hler cone of the latter. We then propose a version of mirror symmetry…
It is conjectured that the existence of constant scalar curvature K\"ahler metrics will be equivalent to K-stability, or K-polystability depending on terminology (Yau-Tian-Donaldson conjecture). There is another GIT stability condition,…
In this paper, we study compactifications of the moduli of smooth del Pezzo surfaces using K-stability and the line arrangement. We construct K-moduli of log del Pezzo pairs with sum of lines as boundary divisors, and prove that for…
We establish the optimal upper bounds for cone angles of K\"ahler-Einstein metrics with conical singularities along smooth anticanonical divisors on smooth K-unstable del Pezzo surfaces.
We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces X and vector fields v which are K-stable in the sense of Berman-Nystrom and therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide some new…
We give an explicit counter-example to a conjecture of Kyusik Hong and Joonyeong Won about $\alpha$-invariants of polarized smooth del Pezzo surfaces of degree one.
We consider projective rational strong Calabi dream surfaces: projective smooth rational surfaces which admit a constant scalar curvature K\"ahler metric for every K\"ahler class. We show that there are only two such rational surfaces,…