Produit eulérien motivique et courbes rationnelles sur les variétés toriques

Abstract : 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.
Complete list of metadatas

Cited literature [24 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00018574
Contributor : David Bourqui <>
Submitted on : Thursday, March 26, 2009 - 10:23:35 AM
Last modification on : Thursday, August 29, 2019 - 3:32:02 PM
Long-term archiving on : Wednesday, September 22, 2010 - 12:28:51 PM

Files

compositio_bourqui_motivique_r...
Files produced by the author(s)

Identifiers

Citation

David Bourqui. Produit eulérien motivique et courbes rationnelles sur les variétés toriques. Compositio Mathematica, Foundation Compositio Mathematica, 2009, 145 (6), pp.1360-1400. ⟨hal-00018574v2⟩

Share

Metrics

Record views

284

Files downloads

283