Lelong numbers on projective varieties

Rodrigo Parra

Displaying similar documents to “Lelong numbers on projective varieties”

A boundedness theorem for morphisms between threefolds

Ekatarina Amerik, Marat Rovinsky, Antonius Van de Ven (1999)

Annales de l'institut Fourier

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The main result of this paper is as follows: let $X, Y$ be smooth projective threefolds (over a field of characteristic zero) such that $b_{2} (X) = b_{2} (Y) = 1$ . If $Y$ is not a projective space, then the degree of a morphism $f : X \to Y$ is bounded in terms of discrete invariants of $X$ and $Y$ . Moreover, suppose that $X$ and $Y$ are smooth projective $n$ -dimensional with cyclic Néron-Severi groups. If $c_{1} (Y) = 0$ , then the degree of $f$ is bounded iff $Y$ is not a flat variety. In particular, to prove our main theorem we show the non-existence of...

Estimates of the number of rational mappings from a fixed variety to varieties of general type

Tanya Bandman, Gerd Dethloff (1997)

Annales de l'institut Fourier

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First we find effective bounds for the number of dominant rational maps $f : X \to Y$ between two fixed smooth projective varieties with ample canonical bundles. The bounds are of the type ${A \cdot K_{X}^{n}}^{{B \cdot K_{X}^{n}}^{2}}$ , where $n = \dim X$ , $K_{X}$ is the canonical bundle of $X$ and $A, B$ are some constants, depending only on $n$ . Then we show that for any variety $X$ there exist numbers $c (X)$ and $C (X)$ with the following properties: For any threefold $Y$ of general type the number of dominant rational maps $f : X \to Y$ is bounded above by $c (X)$ . ...

On projective degenerations of Veronese spaces

Edoardo Ballico (1996)

Banach Center Publications

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Here we give several examples of projective degenerations of subvarieties of $ℙ^{t}$ . The more important case considered here is the d-ple Veronese embedding of $ℙ^{n}$ ; we will show how to degenerate it to the union of $d^{n}$ n-dimensional linear subspaces of $ℙ^{t}; t : = (n + d) / (n! d!) - 1$ and the union of scrolls. Other cases considered in this paper are essentially projective bundles over important varieties. The key tool for the degenerations is a general method due to Moishezon. We will give elsewhere several applications to...

Projective 7-folds with positive defect

Antonio Lanteri, Daniele Struppa (1987)

Compositio Mathematica

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Ahlfors’ currents in higher dimension

Henry de Thélin (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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We consider a nondegenerate holomorphic map $f : V \mapsto X$ where $(X, ω)$ is a compact Hermitian manifold of dimension larger than or equal to $k$ and $V$ is an open connected complex manifold of dimension $k$ . In this article we give criteria which permit to construct Ahlfors’ currents in $X$ .

Hyperbolicity and integral points off divisors in subgeneral position in projective algebraic varieties

Do Duc Thai, Nguyen Huu Kien (2015)

Acta Arithmetica

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The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety $V \subset ℙ_{k ̅}^{m}$ , where k is a number field. As consequences, the results of Ru-Wong (1991), Ru (1993), Noguchi-Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety $V \subset ℙ_{ℂ}^{m} .$

A converse to the Andreotti-Grauert theorem

Jean-Pierre Demailly (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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The goal of this paper is to show that there are strong relations between certain Monge-Ampère integrals appearing in holomorphic Morse inequalities, and asymptotic cohomology estimates for tensor powers of holomorphic line bundles. Especially, we prove that these relations hold without restriction for projective surfaces, and in the special case of the volume, i.e. of asymptotic $0$ -cohomology, for all projective manifolds. These results can be seen as a partial converse to the Andreotti-Grauert...

Families of Measurable Conic Sections in the Projective Space PR

Gioia Failla, Giovanni Molica Bisci (2007)

Bollettino dell'Unione Matematica Italiana

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In this note we prove the measurability of the family of non-degenerate conic sections in the projective space $P^{4}$ , obtained by cutting a non-degenerate quadratic cone by a linear variety of dimension two not containing the cone vertex.