Related papers: Moishezon Manifolds

Suppose $\pi : X \to Y$ is a smooth blow-up along a submanifold $Z$ of $Y$ between complex Fano manifolds $X$ and $Y$ of pseudo-indices $i_X$ and $i_Y$ respectively (recall that $i_X$ is defined by $i_X := \min \{-K_X \cdot C | C {is a…

We shall show that a smooth, quasi-projective variety $X$ has a holomorphically convex universal covering $\wt X$ when (i) $\pi_1(X)$ is residually nilpotent and (ii) there is an admissable variation of \mhs\ over $X$ whose monodromy…

Let $X$ be a metric space and let $\mu$ be a probability measure on it. Consider a Lipschitz map $T: X \rightarrow \Rn$, with Lipschitz constant $\leq 1$. Then one can ask whether the image $TX$ can have large projections on many…

For a smooth projective complex variety $X$, we prove that there exists a birational morphism $X\times X\to Y$ to a projective variety $Y$ contracting the diagonal $\Delta_X\subset X\times X$ to a point if and only if $X$ has maximal…

We classify projective manifolds with flat holomorphic conformal structures.

For every compact K\"ahler manifold $X$ of algebraic dimension $a(X) = \dim X - 1$, we prove that $X$ has arbitrarily small deformations to some projective manifolds.

Miyanishi conjecture claims that for any variety over an algebraically closed field of characteristic zero, any endomorphism of such a variety which is injective outside a closed subset of codimension at least $2$ is bijective. We prove…

It is proved that for a 3-dimensional compact metrizable space X the infinite real projective space is an absolute extensor of X if and only if the real projective plane is an absolute extensor of X.

The present paper mainly presents, for example, explicit classifications of compact smooth manifolds having non-empty boundaries and simple structures where the dimensions are general. Studies of this type is fundamental and important. They…

Let W be a projective variety of dimension n+1, L a free line bundle on W, X in $H^0(L^d)$ a hypersurface of degree d which is generic among those given by sums of monomials from $L$, and let $f : Y \to X$ be a generically finite map from a…

Let $X\subset P^N$ be an n-dimensional connected projective submanifold of projective space. Let $p : P^N\to P^{N-q-1}$ denote the projection from a linear $P^q\subset P^N$. Assuming that $X\not\subset P^q$ we have the induced rational…

This paper generalises Mori's famous theorem about "Projective manifolds with ample tangent bundles" to normal projective varieties in the following way: A normal projective variety over $\mathbb{C}$ with ample tangent sheaf is isomorphic…

In this paper, we establish a structure theorem for a smooth projective variety $X$ with semi-positive holomorphic sectional curvature. Our structure theorem contains the solution for Yau's conjecture and it can be regarded as a natural…

Given a submanifold Z inside X, let Y be the blow-up of X along Z. When the normal bundle of Z in X is convex with a minor assumption, we prove that genus-zero GW-invariants of Y with cohomology insertions from X, are identical to…

In a previous paper we have classified the smooth projective symmetric G-varieties with Picard number one (and G semisimple). In this work we give a geometrical description of such varieties. In particular, we determine their group of…

Many examples of nonpositively curved closed manifolds arise as blow-ups of projective hyperplane arrangements. If the hyperplane arrangement is associated to a finite reflection group W, and the blow-up locus is W-invariant, then the…

Here we explore the geometry of the osculating spaces to projective varieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the…

This article is a survey of recent work of the authors developing a new approach to quantization based on the equivariance with respect to some Lie group of symmetries. Examples are provided by conformal and projective differential…

Using constructions of Voisin, we exhibit a smooth projective variety defined over a number field k and two complex embeddings of k, such that the two complex manifolds induced by these embeddings have non isomorphic cohomology algebras…

Let X be a smooth projective complex variety, of dimension 3, whose Hodge numbers h^{3,0}(X), h^{1,0}(X) both vanish. Let f: X--> X be a birational map that induces an isomorphism on (dense) open subvarieties U,V of X. Then we show that the…