A boundedness theorem for morphisms between threefolds

Ekatarina Amerik; Marat Rovinsky; Antonius Van de Ven

Displaying similar documents to “A boundedness theorem for morphisms between threefolds”

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 $c (X)$ . ...

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 $V \subset ℙ_{ℂ}^{m} .$

Smooth double subvarieties on singular varieties, III

M. R. Gonzalez-Dorrego (2016)

Banach Center Publications

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Let k be an algebraically closed field, char k = 0. Let C be an irreducible nonsingular curve such that rC = S ∩ F, r ∈ ℕ, where S and F are two surfaces and all the singularities of F are of the form $z ³ = x^{3 s} - y^{3 s}$ , s ∈ ℕ. We prove that C can never pass through such kind of singularities of a surface, unless r = 3a, a ∈ ℕ. We study multiplicity-r structures on varieties r ∈ ℕ. Let Z be a reduced irreducible nonsingular (n-1)-dimensional variety such that rZ = X ∩ F, where X is a normal n-fold, F...

Birational positivity in dimension $4$

Behrouz Taji (2014)

Annales de l’institut Fourier

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In this paper we prove that for a nonsingular projective variety of dimension at most 4 and with non-negative Kodaira dimension, the Kodaira dimension of coherent subsheaves of $Ω^{p}$ is bounded from above by the Kodaira dimension of the variety. This implies the finiteness of the fundamental group for such an $X$ provided that $X$ has vanishing Kodaira dimension and non-trivial holomorphic Euler characteristic.

Asymptotics of eigensections on toric varieties

A. Huckleberry, H. Sebert (2013)

Annales de l’institut Fourier

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Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities $| ϕ_{n} |^{2} = | s_{N} |^{2} / | | s_{N} {| |}_{L^{2}}^{2}$ for eigensections $s_{N} \in Γ (X, L^{N})$ approaching a semiclassical ray. Here $X$ is a normal compact toric variety and $L$ is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate...

On Zariski's theorem in positive characteristic

Ilya Tyomkin (2013)

Journal of the European Mathematical Society

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In the current paper we show that the dimension of a family $V$ of irreducible reduced curves in a given ample linear system on a toric surface $S$ over an algebraically closed field is bounded from above by $- K_{S} . C + p_{g} (C) - 1$ , where $C$ denotes a general curve in the family. This result generalizes a famous theorem of Zariski to the case of positive characteristic. We also explore new phenomena that occur in positive characteristic: We show that the equality $𝚍𝚒𝚖 (V) = - K_{S} . C + p_{g} (C) - 1$ does not imply the nodality of $C$ even if $C$ belongs...

Lagrangian fibrations on generalized Kummer varieties

Martin G. Gulbrandsen (2007)

Bulletin de la Société Mathématique de France

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We investigate the existence of Lagrangian fibrations on the generalized Kummer varieties of Beauville. For a principally polarized abelian surface $A$ of Picard number one we find the following: The Kummer variety $K^{n} A$ is birationally equivalent to another irreducible symplectic variety admitting a Lagrangian fibration, if and only if $n$ is a perfect square. And this is the case if and only if $K^{n} A$ carries a divisor with vanishing Beauville-Bogomolov square.

Recovering an algebraic curve using its projections from different points. Applications to static and dynamic computational vision

Jeremy Yirmeyahu Kaminski, Michael Fryers, Mina Teicher (2005)

Journal of the European Mathematical Society

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We study some geometric configurations related to projections of an irreducible algebraic curve embedded in $ℂ ℙ^{3}$ onto embedded projective planes. These configurations are motivated by applications to static and dynamic computational vision. More precisely, we study how an irreducible closed algebraic curve $X$ embedded in $ℂ ℙ^{3}$ , of degree $d$ and genus $g$ , can be recovered using its projections from points onto embedded projective planes. The embeddings are unknown. The only input is the defining...

The projective limit of the $H^{p}$ spaces

J. A. Cima, J. R. Harrington, J. A. Pfaltzgraff (1977)

Colloquium Mathematicae

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The Brauer–Manin obstruction for curves having split Jacobians

Samir Siksek (2004)

Journal de Théorie des Nombres de Bordeaux

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Let $X \to 𝒜$ be a non-constant morphism from a curve $X$ to an abelian variety $𝒜$ , all defined over a number field $k$ . Suppose that $X$ is a counterexample to the Hasse principle. We give sufficient conditions for the failure of the Hasse principle on $X$ to be accounted for by the Brauer–Manin obstruction. These sufficiency conditions are slightly stronger than assuming that $𝒜 (k)$ and $Ш (𝒜 / k)$ are finite.

Polarizations of Prym varieties for Weyl groups via abelianization

Herbert Lange, Christian Pauly (2009)

Journal of the European Mathematical Society

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Let $π : Z \to X$ be a Galois covering of smooth projective curves with Galois group the Weyl group of a simple and simply connected Lie group $G$ . For any dominant weight $λ$ consider the curve $Y = Z / Stab (λ)$ . The Kanev correspondence defines an abelian subvariety $P_{λ}$ of the Jacobian of $Y$ . We compute the type of the polarization of the restriction of the canonical principal polarization of $Jac (Y)$ to $P_{λ}$ in some cases. In particular, in the case of the group $E_{8}$ we obtain families of Prym-Tyurin varieties. The main idea is...

Interpolating discrete multiplicity varieties for $A ⁰_{p} (ℂ ⁿ)$

Bao Qin Li, Enrique Villamor (2006)

Studia Mathematica

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A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space $A ⁰_{p} (ℂ ⁿ)$ .

Special Grassmann manifolds $V_{3}^{4}$ in the projective space $P_{7}$

Josef Vala (1988)

Časopis pro pěstování matematiky

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Semigroup actions on tori and stationary measures on projective spaces

Yves Guivarc&#039;h, Roman Urban (2005)

Studia Mathematica

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Let Γ be a subsemigroup of G = GL(d,ℝ), d > 1. We assume that the action of Γ on $ℝ^{d}$ is strongly irreducible and that Γ contains a proximal and quasi-expanding element. We describe contraction properties of the dynamics of Γ on $ℝ^{d}$ at infinity. This amounts to the consideration of the action of Γ on some compact homogeneous spaces of G, which are extensions of the projective space $ℙ^{d - 1}$ . In the case where Γ is a subsemigroup of GL(d,ℝ) ∩ M(d,ℤ) and Γ has the above properties, we deduce that...