Arithmetic geometry of toric varieties. metrics, measures and heights / José Ignacio Burgos Gil, Patrice Philippon, Martín Sombra.

We show that the height of a toric variety with respect to a toric metrized line bundle can be expressed as the integral over a polytope of a certain adelic family of concave functions. To state and prove this result, we study the Arakelov geometry of toric varieties. In particular, we consider mode...

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Bibliographic Details
Main Authors: Burgos Gil, José I. (José Ignacio), 1962- (Author), Sombra, Martín, 1970- (Author), Philippon, Patrice, 1954- (Author)
Language:English
Language and/or Writing System:
Text in English; abstract also in French.
Published: Paris : Société Mathématique de France, 2014.
Series:Astérisque ; 360.
Subjects:
Toric varieties.
Arakelov theory.
Physical Description:vi, 222 pages : illustrations ; 24 cm.
Format: Book
Contents:
  • Metrized line bundles and their associated heights
  • The Legendre-Fenchel duality
  • Toric varieties
  • Metrics and measures on toric varieties
  • Height of toric varieties
  • Metrics from polytopes
  • Variations on Fubini-Study metrics.