Produit eulérien motivique et courbes rationnelles sur les variétés toriquesReport as inadecuate



 Produit eulérien motivique et courbes rationnelles sur les variétés toriques


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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.



Author: David Bourqui

Source: https://archive.org/







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