Manin's conjecture for toric varieties

Abstract

We prove an asymptotic formula conjectured by Manin for the number of $K$-rational points of bounded height with respect to the anticanonical line bundle for arbitrary smooth projective toric varieties over a number field $K$.

45 pages, LaTeX

Cited by in corpus (12)

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• Cox rings of cubic surfaces and Fano threefolds
• Imaginary quadratic points on toric varieties via universal torsors
• Manin's conjecture for certain spherical threefolds
• Approximation diophantienne et distribution locale sur une surface torique
• Integral points of bounded height on a certain toric variety
• Paucity phenomena for polynomial products
• Endomotives of toric varieties
• On upper bounds of Manin type
• Approximation diophantienne et distribution locale sur une surface torique II
• Counting rational points over number fields on a singular cubic surface
• Asymptotic growth of translation-dilation orbits