相关论文: Canonical complex extensions of K\"ahler manifolds

In this paper, we show that if the holomorphic tangent bundle $TX$ of a compact K\"ahler manifold $X$ is uniformly weakly RC-positive, then $X$ is projective and rationally connected. This result is previously established by Xiaokui Yang…

The aim of this article is to make a first step towards the classification of complex normal affine $\mathbb G_a$-threefolds $X$. We consider the case where the restriction of the quotient morphism $\pi\colon X\to S$ to $\pi^{-1}(S_*)$,…

Let Y be a compact reduced subspace of a complex manifold X, and let F be a subsheaf of the tangent bundle T_X which is closed under the Lie bracket. This paper discusses criteria to guarantee that infinitesimal deformations of the…

In an unpublished preprint, A. King conjectured that there are tilting bundles over projective varieties which are obtained as invariant quotients of affine spaces for linear actions of reductive groups. The goal of this paper is to give…

Classification results for complex Riemannian foliations are obtained. For open subsets of irreducible Hermitian symmetric spaces of compact type, where one has explicit control over the curvature tensor, we completely classify such…

Moment-angle manifolds provide a wide class of examples of non-Kaehler compact complex manifolds. A complex moment-angle manifold Z is constructed via certain combinatorial data, called a complete simplicial fan. In the case of rational…

We obtain a class of locally symmetric Kaehler Einstein structures on the cotangent bundle of a Riemannian manifold of negative sectional curvature. Similar results are obtained in the case of a Riemannian manifold of positive sectional…

Given a measure space ${\mathcal X}$, we can construct a number of induced structures: eg. its $L^2$ space, the space ${\mathcal P}({\mathcal X})$ of probability distributions on ${\mathcal X}$. If, in addition, ${\mathcal X}$ admits a…

Let A be an elliptic curve, and let $V_A$ be the Serre vector bundle on A. A famous example of Demailly-Peternell-Schneider shows that the tautological class of $V_A$ contains a unique closed positive current. In this survey we start by…

Starting with a Z-graded superconnection on a graded vector bundle over a smooth manifold M, we show how Chen's iterated integration of such a superconnection over smooth simplices in M gives an A-infinity functor if and only if the…

We study the cohomological classification of vector bundles on smooth real affine surfaces and threefolds. We show that, as was observed in joint work in A. Asok and J. Fasel and in a coming joint paper with S. Banerjee and J. Fasel, under…

Given a compact quantizable pseudo-K\"ahler manifold $(M,\omega)$ of constant signature, there exists a Hermitian line bundle $(L,h)$ over $M$ with curvature $-2\pi i\,\omega$. We shall show that the asymptotic expansion of the Bergman…

In this paper, we consider a compact Kahler manifold with extremal Kahler metric and a Mumford stable holomorphic bundle over it. We proved that, if the holomorphic vector field defining the extremal Kahler metric is liftable to the bundle…

We discuss algebraic vector bundles on smooth k-schemes X contractible from the standpoint of A^1-homotopy theory; when k = C, the smooth manifolds X(C) are contractible as topological spaces. The integral algebraic K-theory and integral…

We conjecture that any perverse sheaf on a compact aspherical K\"ahler manifold has non-negative Euler characteristic. This extends the Singer-Hopf conjecture in the K\"ahler setting. We verify the stronger conjecture when the manifold X…

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 $q\le\dim(X)+1$.

Given a family $f:\mathcal X \to S$ of canonically polarized manifolds, the unique K\"ahler-Einstein metrics on the fibers induce a hermitian metric on the relative canonical bundle $\mathcal K_{\mathcal X/S}$. We use a global elliptic…

We prove that any holomorphic vector bundle admitting a holomorphic connection, over a compact K\"ahler Calabi-Yau manifold, also admits a flat holomorphic connection. This addresses a particular case of a question asked by Atiyah and…

Generalising a classical theorem by Ueno, we prove structure results for manifolds with nef or semiample cotangent bundle.

We are concerned in this article with a classical question in spectral geometry dating back to McKean-Singer, Patodi and Tanno: whether or not the constancy of holomorphic sectional curvature of a complex $n$-dimensional compact K\"ahler…