Algebraic points, non-anticanonical heights and the Severi problem on toric varieties

Abstract : 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.
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Submitted on : Thursday, December 1, 2016 - 2:51:40 PM
Last modification on : Friday, November 16, 2018 - 1:21:47 AM

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David Bourqui. Algebraic points, non-anticanonical heights and the Severi problem on toric varieties. Proceedings of the London Mathematical Society, London Mathematical Society, 2016, 113 (4), pp.474 - 514. ⟨10.1112/plms/pdw035⟩. ⟨hal-01406713⟩

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