Produit eulérien motivique et courbes rationnelles sur les variétés toriques

Details Produit eulérien motivique et courbes rationnelles sur les variétés toriques Produit eulérien motivique et courbes rationnelles sur les variétés toriques

2006-02-06

arxiv.org/abs/math/0602094v2

Mathematics

Number Theory

Scientific paper

We 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 eulerian motivic product. It relies on a construction of Denef and Loeser which associates a virtual motive to a first order logic ring formula.

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