Arithmetic geometry of toric varieties metrics, measures and heights
Metrized line bundles and their associated heightsThe Legendre-Fenchel duality -- Toric varieties -- Metrics and measures on toric varieties -- Height of toric varieties -- Metrics from polytopes -- Variations on Fubini-Study metrics.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , |
| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Paris
Soc. Math. de France
2014
|
| Schriftenreihe: | Astérisque
360 |
| Schlagworte: | |
| Online Zugang: | Inhaltstext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Tag hinzufügen | Zusammenfassung: | Metrized line bundles and their associated heightsThe Legendre-Fenchel duality -- Toric varieties -- Metrics and measures on toric varieties -- Height of toric varieties -- Metrics from polytopes -- Variations on Fubini-Study metrics. 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 models over a discrete valuation ring, metrized line bundles, and their associated measures and heights. We show that these notions can be translated in terms of convex analysis, and are closely related to objects like polyhedral complexes, concave functions, real Monge-Ampère measures, and Legendre-Fenchel duality. We also present a closed formula for the integral over a polytope of a function of one variable composed with a linear form. This formula allows us to compute the height of toric varieties with respect to some interesting metrics arising from polytopes. We also compute the height of toric projective curves with respect to the Fubini-Study metric and the height of some toric bundles"--Page 4 of cover |
|---|---|
| Beschreibung: | Literaturverz. S. [207] - 212 |
| Beschreibung: | VI, 222 Seiten Diagramme |
| ISBN: | 9782856297834 978-2-85629-783-4 |