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Rational points of bounded height on Fano varieties

- J. Franke, Y. Manin, Y. Tschinkel
- Mathematics
- 1 June 1989

a prime pe7Z. Let V be an algebraic variety defined over F and lI~ a metrized line bundle on V, i.e., a system (L, ]'],) consisting of a line bundle L and a family of Banach v-adic metrics on L | F,,… Expand

Manin's conjecture for toric varieties

- V. Batyrev, Y. Tschinkel
- Mathematics
- 1 October 1995

We prove an asymptotic formula conjectured by Manin for the number of $K$-rational points of bounded height with respect to the anticanonical line bundle for arbitrary smooth projective toric… Expand

Tamagawa numbers of polarized algebraic varieties

- V. Batyrev, Y. Tschinkel
- Mathematics
- 1 December 1997

Let ${\cal L} = (L, \| \cdot \|_v)$ be an ample metrized invertible sheaf on a smooth quasi-projective algebraic variety $V$ defined over a number field. Denote by $N(V,{\cal L},B)$ the number of… Expand

Rational points on some Fano cubic bundles

- V. Batyrev, Y. Tschinkel
- Mathematics
- 1 February 1996

Nous considerons des hypersurfaces de Fano X n+2 ⊂ P n x P 3 (n ≥ 1) donnees par un polynome Formula math ou l 0 (x)..... l 3 (x) sont des formes lineaires homogenes en x 0 ..... x n . Nous obtenons… Expand

Density of rational points on elliptic K3 surfaces

- F. Bogomolov, Y. Tschinkel
- Mathematics
- 15 February 1999

Let $X$ be a K3 surface defined over a number field $K$. Assume that $X$ admits a structure of an elliptic fibration or an infinite group of automorphisms. Then there exists a finite extension $K'/K$… Expand

On the distribution of points of bounded height on equivariant compactifications of vector groups

- Antoine Chambert-Loir, Y. Tschinkel
- Mathematics
- 2 May 2000

Abstract.We prove asymptotic formulas for the number of rational points of bounded height on smooth equivariant compactifications of the affine space.

Moving and Ample Cones of Holomorphic Symplectic Fourfolds

- B. Hassett, Y. Tschinkel
- Mathematics
- 1 October 2007

We analyze the ample and moving cones of holomorphic symplectic manifolds, in light of recent advances in the minimal model program. As an application, we establish a numerical criterion for… Expand

Mori cones of holomorphic symplectic varieties of K3 type

- Arend Bayer, B. Hassett, Y. Tschinkel
- Mathematics
- 8 July 2013

We determine the Mori cone of holomorphic symplectic varieties deformation equivalent to the punctual Hilbert scheme on a K3 surface. Our description is given in terms of Markman's extended Hodge… Expand

Geometry of equivariant compactifications of $G^n_a$

- B. Hassett, Y. Tschinkel
- Mathematics
- 11 February 1999

Equivariant compactifications of reductive groups can be described by combinatorial data. On the other hand, equivariant compactifications of the additive group G^n_a are more complicated in at least… Expand

Stable rationality of quadric surface bundles over surfaces

- B. Hassett, A. Pirutka, Y. Tschinkel
- Mathematics
- 30 March 2016

We study rationality properties of quadric surface bundles over the projective plane. We exhibit families of smooth projective complex fourfolds of this type over connected bases, containing both… Expand

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