Related papers: Arc K-semistability is a very general property

Let $K$ be a complete discrete valuation field. Let $\mathcal{O}_K$ be its ring of integers. Let $k$ be its residue field which we assume to be algebraically closed of characteristic exponent $p\geq1$. Let $G/K$ be a semi-abelian variety.…

In the first part we extend the construction of the smooth normal-crossing divisors compactification of projectivized strata of abelian differentials given by Bainbridge, Chen, Gendron, Grushevsky and Moeller to the case of k-differentials.…

We consider generalized metric spaces taking distances in an arbitrary ordered commutative monoid, and investigate when a class $\mathcal{K}$ of finite generalized metric spaces satisfies the Hrushovski extension property: for any…

In this paper, we discuss stable pairs, which were first studied by S. Paul, and give a proof for a result I learned from him. As a consequence, we will show that the K-stability implies the CM-stability.

This paper contains two results concerning the equivariant K-theory of toric varieties. The first is a formula for the equivariant K-groups of an arbitrary affine toric variety, generalizing the known formula for smooth ones. In fact, this…

A rigidity result for normal rectifiable $k$-chains in $\mathbb{R}^n$ with coefficients in an Abelian normed group is established. Given some decompositions $k=k_1+k_2$, $n=n_1+n_2$ and some rectifiable $k$-chain $A$ in $\mathbb{R}^n$, we…

In this paper, we proved that a log smooth family of log general type klt pairs with a special (in the sense of Campana) quasi-projective base is isotrivial. As a consequence, we proved the generalized Kebekus-Kov\'acs conjecture…

We prove that an extremal metric on a polarised smooth complex projective variety exists if it is $\mathbb{G}$-uniformly $K$-stable relative to the extremal torus over models, extending a result due to Chi Li for constant scalar curvature…

We generalise partial results about the Yau-Tian-Donaldson correspondence on ruled manifolds to bundles whose fibre is a classical flag variety. This is done using Chern class computations involving the combinatorics of Schur functors. The…

In this paper, we investigate the geometry of the orbit space of the closure of the subscheme parametrizing smooth Fano K\"ahler-Einstein manifolds inside an appropriate Hilbert scheme. In particular, we prove that being K-semistable is a…

This paper is concerned with the model-theoretic study of pairs $(K,F)$ where $K$ is an algebraically closed field and $F$ is a distinguished subfield of $K$ allowing extra structure. We study the basic model-theoretic properties of those…

We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…

We give a new proof of the fact that the condition of a Fano manifold admitting a K\"ahler-Einstein metric is Zariski-open (provided that the automorphism group is discrete). This proof does not use the characterisation involving stability.…

A product of K\"ahler manifolds also carries a K\"ahler metric. In this short note we would like to study the product of generalized $p-$K\"ahler manifolds, compact or not. The results we get extend the known results (balanced, SKT, sG…

The main geometric result of this paper is that given any family of surfaces of general type f:X-->B, for sufficiently large n the fiber product X^n_B dominates a variety of general type. This result is especially interesting when it is…

Ross and Thomas have shown that subschemes can K-destabilise polarised varieties, yielding a notion known as slope (in)stability for varieties. Here we describe a special situation in which slope instability for varieties (for example of…

The aim of this paper is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a $k$-algebra and this new ``$k$-space'' becomes a generalization of the…

Let $K$ be a finite extension of $\mathbb{Q}_p$, and choose a uniformizer $\pi\in K$, and put $K_\infty:=K(\sqrt[p^\infty]{\pi})$. We introduce a new technique using restriction to $\Gal(\ol K/K_\infty)$ to study flat deformation rings. We…

We investigate basic properties of uniformly rational varieties, i.e. those smooth varieties for which every point has a Zariski open neighborhood isomorphic to an open subset of A^n. It is an open question of Gromov whether all smooth…

In this paper, we will consider a generalization of Bogomolov's inequality and Cornalba-Harris-Bost's inequality to semistable families of arithmetic varieties under the idea that geometric semistability implies a certain kind of arithmetic…