相关论文: Dynamical construction of K\"{a}hler-Einstein metr…

We consider balanced metrics on complex manifolds with holomorphically trivial canonical bundle, most commonly known as balanced $\rm{SU}(n)$-structures. Such structures are of interest for both Hermitian geometry and string theory, since…

On a 3-manifold bounding a compact 4-manifold, let a conformal structure be induced from a complete Einstein metric which conformally compactifies to a K\"ahler metric. Formulas are derived for the eta invariant of this conformal structure…

The classical Hurwitz spaces, that parameterize compact Riemann surfaces equipped with covering maps to ${\mathbb P}_1$ of fixed numerical type with simple branch points, are extensively studied in the literature. We apply deformation…

A flat complex vector bundle (E,D) on a compact Riemannian manifold (X,g) is stable (resp. polystable) in the sense of Corlette [C] if it has no D-invariant subbundle (resp. if it is the D-invariant direct sum of stable subbundles). It has…

The aim of this paper is to study Seifert bundle structures on simply connected 5--manifolds. We classify all such 5--manifolds which admit a Seifert bundle structure, and in a few cases all Seifert bundle structures are also classified.…

We prove the existence of non-positively curved K\"ahler-Einstein metrics with cone singularities along a given simple normal crossing divisor on a compact K\"ahler manifold, under a technical condition on the cone angles, and we also…

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…

We obtain necessary conditions for the existence of special K\"ahler structures with isolated singularities on compact Riemann surfaces. We prove that these conditions are also sufficient in the case of the Riemann sphere and, moreover, we…

A simple geometric procedure is proposed for constructing Wick symbols on cotangent bundles to Riemannian manifolds. The main ingredient of the construction is a method of endowing the cotangent bundle with a formal K\"ahler structure. The…

We study the quantization of coupled K\"ahler-Einstein (CKE) metrics, namely we approximate CKE metrics by means of the canonical Bergman metrics, so called the ``balanced metrics''. We prove the existence and weak convergence of balanced…

Solutions to vacuum Einstein field equations with cosmological constant, such as the de Sitter space and the anti-de Sitter space, are basic in different cosmological and theoretical developments. It is also well known that complex…

We construct new explicit toric scalar-flat K{\"a}hler ALE metrics on weighted projective spaces of non-compact type, which we use to obtain smooth extremal K{\"a}hler metrics on appropriate resolutions of orbifolds. In particular, we…

For $U(2)$-invariant 4-metrics, we show that the $B^t$-flat metrics are very different from the other canonical metrics (Bach-flat, Einstein, extremal K\"ahler, etc). We show every $U(2)$-invariant metric is conformal to two separate…

Let L be a holomorphic line bundle over a compact complex projective Hermitian manifold X. Any fixed smooth hermitian metric h on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k th tensor…

We give a $K$-theoretic criterion for a quasi-projective variety to be smooth. If $\mathbb{L}$ is a line bundle corresponding to an ample invertible sheaf on $X$, it suffices that $K_q(X) = K_q(\mathbb{L})$ for all $q\le\dim(X)+1$.

We give an explicit description of the syntomic elliptic polylogarithm on the universal elliptic curve over the ordinary locus of the modular curve in terms of certain $p$-adic analytic moment functions associated to Katz' two-variable…

We study Einstein metrics on complex projective spaces that are invariant under cohomogeneity one actions of compact connected Lie groups, under the assumption that the singular orbits are totally geodesic. These actions were classified by…

We introduce a new Hermitian metric on the cohomology ring of compact K\"ahlerian manifolds with a pair $(v,w)$ satisfying certain Hodge-Riemann relations. An Hermitian metric on the exterior algebra of the cotangent bundle is also defined…

We obtain a locally symmetric Kaehler Einstein structure on the cotangent bundle of a Riemannian manifold of negative constant sectional curvature. Similar results are obtained on a tube around zero section in the cotangent bundle, in the…

The cohomology algebra of the canonical bundle of a compact K\"ahler manifold is naturally viewed as a module over an exterior algebra. We use the Bernstein-Gel'fand-Gel'fand correspondence, together with Generic Vanishing theory, in order…