Related papers: K-stability of cubic threefolds

For a finite subgroup G in SL(3,C), Bridgeland, King and Reid proved that the moduli space of G-clusters is a crepant resolution of the quotient C^3/G. This paper considers the moduli spaces M_\theta, introduced by Kronheimer and further…

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…

We characterize the image of the period map for cubic fourfolds with at worst simple singularities as the complement of an arrangement of hyperplanes in the period space. It follows then that the GIT compactification of the moduli space of…

We show that the K-moduli spaces of log Fano pairs $(\mathbb{P}^3, cS)$ where $S$ is a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily-Borel compactification of moduli of quartic K3 surfaces as $c$…

In [Ma1] S. Ma established a bijection between Fourier--Mukai partners of a K3 surface and cusps of the K\"ahler moduli space. The K\"ahler moduli space can be described as a quotient of Bridgeland's stability manifold. We study the…

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 the moduli space of quasi-polarized complex K3 surfaces of degree 6 and 8 via geometric invariant theory. The general members in such moduli spaces are complete intersections in projective spaces and we have natural…

The aim of this paper is to study the singularities of certain moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver varieties. The singularities in question arise from the choice of a non--generic polarization, with respect…

We find Fano threefolds $X$ admitting K\"ahler-Ricci solitons (KRS) with non-trivial moduli, which are $\mathbb{T}$-varieties of complexity two. More precisely, we show that the weighted K-stability of $(X,\xi_0)$ (where $\xi_0$ is the…

We show that the GIT quotients of suitable loci in the Hilbert and Chow schemes of 4-canonically embedded curves of genus $g\ge 3$ are the moduli space $\bar{M}_g^{\text{ps}}$ of pseudo-stable curves constructed by Schubert in…

In this paper we compute the cohomology of moduli space of cubic fourfolds with ADE type singularities relying on Kirwan's blowup and Laza's GIT construction. More precisely, we obtain the Betti numbers of Kirwan's resolution of the moduli…

This largely expository paper first gives an introduction to Hilbert stability and its use in Gieseker's GIT construction of $\overline{M}_g$. Then I review recent work in this area--variants for unpointed curves that arise in Hassett's log…

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.

We announce an explicit description of the strictly semistable boundary of the GIT moduli space of quintic threefolds. For the natural action of \(\mathrm{SL}(5)\) on \(\mathbb P(\mathrm{Sym}^5\mathbb C^5)\), we classify the 38 boundary…

We formulate a notion of K-stability for K\"ahler manifolds, and prove one direction of the Yau-Tian-Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. coercive) implies…

We study logarithmic K-stability for pairs by extending the formula for Donaldson-Futaki invariants to log setting. We also provide algebro-geometric counterparts of recent results of existence of Kahler-Einstein metrics with cone…

We prove that the existence of constant scalar curvature K\"ahler metrics with cone singularities along a divisor implies log $K$-polystability and $G$-uniform log $K$-stability, where $G$ is the automorphism group which preserves the…

In this paper, we make a generalization of the results in \cite{Li22a} to the singular and weighted setting. In particular, we show that on a polarized projective klt variety, the $\mathbb{G}$-uniform weighted K-stability for models implies…

We describe a compactification by KSBA stable pairs of the five-dimensional moduli space of K3 surfaces with purely non-symplectic automorphism of order four and $U(2)\oplus D_4^{\oplus2}$ lattice polarization. These K3 surfaces can be…

We prove continuity results for new stability thresholds related to uniform K-stability and deduce that uniform K-stability is an open condition in the K\"ahler cone of any compact K\"ahler manifold, thus establishing an algebro-geometric…