相关论文: On the boundary behavior of K\"ahler-Einstein metr…

For a holomorphic vector bundle $E$ over a polarised K\"ahler manifold, we establish a direct link between the slope stability of $E$ and the asymptotic behaviour of Donaldson's functional, by defining the Quot-scheme limit of Fubini-Study…

The total space of the tangent bundle of a K\"ahler manifold admits a canonical K\"ahler structure. Parallel translation identifies the space ${\Bbb{T}}$ of oriented affine lines in ${\Bbb{R}}^3$ with the tangent bundle of $S^2$. Thus, the…

Let (X,[\omega]) be a compact Kaehler manifold with a fixed Kaehler class [\omega]. Let K_\omega be the set of all Kaehler metrics on X whose Kaehler class equals [\omega]. In this paper we investigate the critical points of the functional…

It is well known that the Grauert-Riemenschneider canonical sheaf $\mathcal{K}_X$ of holomorphic square-integrable $n$-forms is a central tool in $L^2$-theory for the $\overline\partial$-operator on a singular complex space $X$ of pure…

A Poincar\'e type K\"ahler metric on the complement X\D of a simple normal crossing divisor D, in a compact K\"ahler manifold X, is a K\"ahler metric on X\D with cusp singularity along D. We relate the Futaki character for holomorphic…

In this paper, we study the stability of the conical K\"ahler-Ricci flows on Fano manifolds. That is, if there exists a conical K\"ahler-Einstein metric with cone angle $2\pi\beta$ along the divisor, then for any $\beta'$ sufficiently close…

Recent advances in quantitative unique continuation properties for solutions to uniformly elliptic, divergence form equations (with Lipschitz coefficients) has led to a good understanding of the vanishing order and size of singular and zero…

We discuss how metric limits and rescalings of K\"ahler-Einstein metrics connect with Algebraic Geometry, mostly in relation to the study of moduli spaces of varieties, and singularities. Along the way, we describe some elementary examples,…

Let $(X,L_{X})$ be an $n$-dimensional polarized manifold. Let $D$ be a smooth hypersurface defined by a holomorphic section of $L_{X}$. In this paper, we show the existence of a complete K\"{a}hler metric on $X \setminus D$ whose scalar…

Motivated by Shokurov's ACC Conjecture for log canonical thresholds, we propose an inductive point of view on singularities of pairs, in the case when the ambient variety is smooth. Our main result characterizes the log canonicity of a pair…

We consider coupled K\"ahler-Einstein metrics and weighted solitons on Fano manifolds. These are natural generalizations of K\"ahler-Einstein metrics. As in the case of K\"ahler-Einstein metrics, the existence is known to be equivalent to…

Given a log canonical pair $(X, \Delta)$, we show that $K_X+\Delta$ is nef assuming there is no non-constant map from the affine line with values in the open strata of the stratification induced by the non-klt locus of $(X, \Delta)$. This…

Using an ansatz due to LeBrun we construct complete scalar-flat K\"ahler metrics with a prescribed varying conical singularity along a divisor.

Inspired by a parabolic system of Li-Yuan-Zhang and the continuity equation of La Nave-Tian, we study a system of elliptic equations for a K\"ahler metric $\omega$ and a closed $(1, 1)$-form $\alpha$. Assuming a uniform estimate for…

Recently Johnson and Koll\'ar determined the complete list of anticanonically embedded quasi smooth log del Pezzo surfaces in weighted projective 3-spaces. They also proved that many of those surfaces admit a K\"ahler-Einstein metric, and…

The Ricci curvature of the Bergman metric on a bounded domain $D\subset \mathbb{C}^n$ is strictly bounded above by $n+1$ and consequently $\log (K_D^{n+1}g_{B,D})$, where $K_D$ is the Bergman kernel for $D$ on the diagonal and $g_{B, D}$ is…

This paper investigates the representation-theoretic structure of the Koszul cohomology of a smooth projective variety $X$ over an algebraically closed field $k$, admitting an action of a finite group $G$ of order coprime to ${\rm…

In the present paper and the companion paper [9] a probabilistic (statistical-mechanical) approach to the construction of canonical metrics on a complex algebraic varieties X is introduced, by sampling "temperature deformed" determinantal…

We prove bounds in the strict local $L^{2}(\mathbb{R}^{d})$ range for trilinear Fourier multiplier forms with a $d$-dimensional singular subspace. Given a fixed parameter $K \ge 1$, we treat multipliers with non-degenerate singularity that…

We show that for each fixed dimension $d\geq 2$, the set of $d$-dimensional klt elliptic varieties with numerically trivial canonical bundle is bounded up to isomorphism in codimension one, provided that the torsion index of the canonical…