Related papers: Uniqueness of CP^n

Let K be a compact semi-simple Lie group. We classify K-invariant Kaehler structures on the space Kc/(P,P), where Kc is the complexification of K, P is a parabolic subgroup of Kc, and (P,P) the commutator subgroup. For each Kaehler…

The main result of this paper is a characterization of properly infinite injective von Neumann algebras and of nuclear C*-algebras by using a uniqueness theorem, based on generalizations of Voiculescu's famous Weyl-von Neumann theorem.

This is an expository article on the singularities of nilpotent orbit closures in simple Lie algebras over the complex numbers. It is slanted towards aspects that are relevant for representation theory, including Maffei's theorem relating…

We give a method to construct Calabi-Yau metrics on G-invariant vector bundles over Kahler coset spaces G/H using supersymmetric nonlinear realizations with matter coupling. As a concrete example we discuss the CP^N model coupled with…

We prove that the irreducible components of the moduli space of polarized Calabi-Yau pairs are projective.

For the Jacobian of a curve, the Riemann singularity theorem gives a geometric interpretation of the singularities of the theta divisor in terms of special linear series on the curve. This paper proves an analogous theorem for Prym…

We prove that the space of convex real projective structures on a surface of genus $g\ge 2$ admits a mapping class group invariant K\"ahler metric where Teichm\"uller space with Weil-Petersson metric is a totally geodesic complex…

It was recently discovered that Killing horizons in the generic Kerr-NUT-(anti) de Sitter spacetimes are projectively singular, i.e. their spaces of the null generators have singular geometry. Only if the cosmological constant takes the…

A recent theorem of Diverio--Trapani and Wu--Yau asserts that a compact K\"ahler manifold with a K\"ahler metric of quasi-negative holomorphic sectional curvature is projective and canonically polarized. This confirms a long-standing…

The purpose of this article is to show uniqueness theorems for meromorphic mappings of C^m to CP^n with few hyperplanes H_j, j=1,...,q. It is well known that uniqueness theorems hold for q \geq 3n+2. In this paper we show that for every…

We show that 1-D rarefaction wave solutions are unique in the class of bounded entropy solutions to the multidimensional compressible Euler system. Such a result may be viewed as a counterpart of the recent examples of non-uniqueness of the…

Recent progress in understanding the structure of cosmological singularities is reviewed. The well-known picture due to Belinskii, Khalatnikov and Lifschitz (BKL) is summarized briefly and it is discussed what existing analytical and…

We prove the equisingular rigidity of the singular Hirzebruch-Kummer coverings $X(n, \mathcal{L})$ of the projective plane branched on line configurations $\mathcal{L}$, satisfying some technical condition. In the case, $\mathcal{L}$ = the…

In the framework of special Kahler geometry we consider the supergravity-matter system which emerges on a K3-fibered Calabi-Yau manifold. By applying the rigid limit procedure in the vicinity of a conifold singularity we compute the Kahler…

In this article we study the cohomological and homological (due to Jannsen) Hodge conjecture for singular varieties. The motivation for studying singular varieties comes from the fact that any smooth projective variety X is birational to a…

Let X be the quotient of a smooth projective variety over a field by a finite group action (in which case we say X is pseudo-smooth), such that the singularities of X are isolated k-rational points. Let Y be obtained by blowing up these…

We show that a compact Kahler manifold with nonpositive holomorphic sectional curvature has nef canonical bundle. If the holomorphic sectional curvature is negative then it follows that the canonical bundle is ample, confirming a conjecture…

Kempf proved that the theta divisor of a smooth projective curve C has rational singularities. In this paper we estimate the dimensions of the jet schemes of the theta divisor and show that all these schemes are irreducible. In particular,…

We prove the Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds, that is, for projective manifolds equipped with a holomorphic action of a compact Lie group with at least one real hypersurface orbit. Contrary to what seems to be…

This paper is devoted to the problem of recovering a potential $q$ in a domain in $\mathbb{R}^d$ for $d \geq 3$ from the Dirichlet to Neumann map. This problem is related to the inverse Calder\'on conductivity problem via the Liouville…