Algebraic points, non-anticanonical heights and the Severi problem on toric varieties. (English) Zbl 1427.14108
Summary: In this article, we apply counting formulas for the number of morphisms from a curve to a toric variety to three different though related contexts (the first two are to be understood over global function fields): Manin’s problem for rational points of bounded non-anticanonical height, asymptotics for algebraic points of bounded height and irreducibility of certain moduli spaces of curves, with application to the Severi problem for toric surfaces.
MSC:
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
| 14H10 | Families, moduli of curves (algebraic) |
| 11G50 | Heights |
| 11G35 | Varieties over global fields |
Keywords:
Severi problemReferences:
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