Résumé
Deux variétés K-équivalentes sont-elles isomorphes par morceaux? Dans cet article, nous étudions cette question. Nous obtenons une réponse positive, en toute dimension, dans le cas où les lieux exceptionnels sont de petite dimension.
Abstract
Are two smooth K-equivalent varieties piecewise isomorphic? In this article, we study this question. We obtain a positive partial answer, in every dimension, but when the exceptional loci are of small dimension.
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Références
Beauville A. et al.: Variétés stablement rationnelles non rationnelles. Ann. of Math. 121, 283–318 (1985)
Denef J., Loeser F.: Germs of arcs on singular algebraic varieties and motivic integration. Invent. Math. 135, 201–232 (1999)
Larsen M., Lunts V.A.: Motivic measures and stable birational geometry. Mosc. Math. J. 3, 85–95 (2003)
Q. Liu and J. Sebag, The Grothendieck ring of varieties and piecewise isomorphisms, à paraî tre dans Math. Z. (2009).
J. Sebag, Variations on a question of Larsen and Lunts, à paraî tre dans, Proc. Amer. Math. Soc. (2009).
Sebag J.: Intégration motivique sur les schémas formels. Bull. Soc. Math. France 132, 1–54 (2004)
W. Veys, Arc spaces, motivic integration and stringy invariants, Singularity theory and its applications, Adv. Stud. Pure Math., 43 (2006), Math. Soc. Japan, Tokyo, 529–572.
Wang C.-L.: On the topology of birational minimal models. J. Differential Geom. 50, 129–146 (1998)
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Sebag, J. Variétés K-équivalentes et géométrie par morceaux. Arch. Math. 94, 207–217 (2010). https://doi.org/10.1007/s00013-009-0095-3
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DOI: https://doi.org/10.1007/s00013-009-0095-3