Produit eulérien motivique et courbes rationnelles sur les variétés toriques
2009 ◽
Vol 145
(6)
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pp. 1360-1400
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AbstractWe study the asymptotical behaviour of the moduli space of morphisms of given anticanonical degree from a rational curve to a split toric variety, when the degree goes to infinity. We obtain in this case a geometric analogue of Manin’s conjecture about rational points of bounded height on varieties defined over a global field. The study is led through a generating series whose coefficients lie in a Grothendieck ring of motives, the motivic height zeta function. In order to establish convergence properties of this function, we use a notion of motivic Euler product. It relies on a construction of Denef and Loeser which associates a virtual motive to a first order logic ring formula.
2009 ◽
Vol 19
(12)
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pp. 3091-3099
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2018 ◽
Keyword(s):
Keyword(s):
2019 ◽
Vol 29
(8)
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pp. 1311-1344
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Keyword(s):
Keyword(s):