Heights and reductions of semi-stable varieties

Shouwu Zhang

Displaying similar documents to “Heights and reductions of semi-stable varieties”

Successive minima on arithmetic varieties

C. Soulé (1995)

Compositio Mathematica

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Local and canonical heights of subvarieties

Walter Gubler (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Classical results of Weil, Néron and Tate are generalized to local heights of subvarieties with respect to hermitian pseudo-divisors. The local heights are well-defined if the intersection of supports is empty. In the archimedean case, the metrics are hermitian and the local heights are defined by a refined version of the $*$ -product of Gillet-Soulé developped on compact varieties without assuming regularity. In the non-archimedean case, the local heights are intersection numbers using...

Remarks on integral inequalities on complex manifolds

Edoardo Vesentini (1966)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Perturbations of the metric in Seiberg-Witten equations

Luca Scala (2011)

Annales de l’institut Fourier

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Let $M$ a compact connected oriented 4-manifold. We study the space $Ξ$ of ${Spin}^{c}$ -structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on $M$ . In order to study perturbations of the metric in Seiberg-Witten equations, we study the transversality of universal equations, parametrized with all ${Spin}^{c}$ -structures $Ξ$ . We prove that, on a complex Kähler surface, for an hermitian metric $h$ sufficiently close to the original Kähler metric, the...

Diophantine approximation on algebraic varieties

Michael Nakamaye (1999)

Journal de théorie des nombres de Bordeaux

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We present an overview of recent advances in diophantine approximation. Beginning with Roth's theorem, we discuss the Mordell conjecture and then pass on to recent higher dimensional results due to Faltings-Wustholz and to Faltings respectively.

Eta invariants and complex immersions

Jean-Michel Bismut (1990)

Bulletin de la Société Mathématique de France

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Algebraic leaves of algebraic foliations over number fields

Jean-Benoît Bost (2001)

Publications Mathématiques de l'IHÉS

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We prove an algebraicity criterion for leaves of algebraic foliations defined over number fields. Namely, consider a number field $K$ embedded in $C$ , a smooth algebraic variety $X$ over $K$ , equipped with a $K -$ rational point $P$ , and $F$ an algebraic subbundle of the its tangent bundle $T_{X}$ , defined over $K$ . Assume moreover that the vector bundle $F$ is involutive, i.e., closed under Lie bracket. Then it defines an holomorphic foliation of the analytic manifold $X (C)$ , and one may consider its leaf $F$ through...