相关论文: K-stable divisors in $\mathbb{P}^1\times\mathbb{P}…

We find all K-polystable limits of divisors in $(\mathbb{P}^1)^4$ of degree $(1,1,1,1)$ and explicitly describe the associated irreducible component of the K-moduli space.

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 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…

For every integer $a \geq 2$, we relate the K-stability of hypersurfaces in the weighted projective space $\mathbb{P}(1,1,a,a)$ of degree $2a$ with the GIT stability of binary forms of degree $2a$. Moreover, we prove that such a…

We prove K-stability for infinitely many smooth members of the family 2.19 of the Mukai-Mori classification.

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 classify normal stable surfaces with $K_X^2 = 1$, $p_g = 2$ and $q=0$ with a unique singular point which is a non-canonical T-singularity, thus exhibiting two divisors in the main component and a new irreducible component of the moduli…

In an algebro-geometric way, we completely determine whether smooth del Pezzo surfaces are K-(semi)stable or not.

We prove K-stability of every smooth member of the family 2.15 of the Mukai-Mori classification.

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…

We show that a polarised manifold with a constant scalar curvature K\"ahler metric and discrete automorphisms is K-stable. This refines the K-semistability proved by S. K. Donaldson.

We describe a procedure to compute the rational nonstable K-groups of A$\mathbb{T}$-algebras. As an application, we show that an A$\mathbb{T}$-algebra is K-stable if and only if it has slow dimension growth.

In this paper, we prove that any polarized K-stable manifold is CM-stable. This extends what I did for Fano manifolds in my 2012 paper.

We study slope stability of smooth surfaces and its connection with exceptional divisors. We show that a surface containing an exceptional divisor with arithmetic genus at least two is slope unstable for some polarisation. In the converse…

We describe the GIT compactification of the moduli of (2,2)-type effective divisors of $\mathbb{P}^1\times\mathbb{P}^2$ (i.e., surfaces of the linear system $\vert \pi_1^*\mathcal{O}_{\mathbb{P}^1}(2)\otimes…

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

We prove that existence of a k-rational point can be detected by the stable A^1-homotopy category of S^1-spectra, or even a "rationalized" variant of this category.

An asymptotic formula is proved for the k-fold divisor function averaged over homogeneous polynomials of degree k in k-1 variables coming from incomplete norm forms.

Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state. Let A != 0 be a unital C^*-algebra with A = A tensor Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants,…

We introduce a theory of uniform K-stability for big line bundles on smooth projective varieties. This extends the existing theory both for varieties with ample line bundles, and for varieties with big anticanonical class. Our main result…