Nash blow-ups of jet schemes  [ Éclatements de Nash des espaces de jets ]
Annales de l'Institut Fourier, Tome 69 (2019) no. 6, pp. 2577-2588.

Étant donné un morphisme birationnel projectif de variétés nous fournissons une manière explicite et naturelle de construire des compactifications relatives des applications induites sur les composantes principales des espaces de jets. Dans le cas où le morphisme est l’éclatement de Nash d’une variété, nous montrons que ces compactifications relatives sont données par les éclatements de Nash des composantes principales des espaces de jets.

Given an arbitrary projective birational morphism of varieties, we provide a natural and explicit way of constructing relative compactifications of the maps induced on the main components of the jet schemes. In the case the morphism is the Nash blow-up of a variety, such relative compactifications are shown to be given by the Nash blow-ups of the main components of the jet schemes.

Reçu le : 2017-12-03
Révisé le : 2018-10-05
Accepté le : 2019-01-16
Publié le : 2019-10-29
DOI : https://doi.org/10.5802/aif.3302
Classification : 14E18,  14E04,  14B05
Mots clés: Espace de jets, éclatement de Nash, singularités, Grassmanienne, foncteur de points
@article{AIF_2019__69_6_2577_0,
     author = {de Fernex, Tommaso and Docampo, Roi},
     title = {Nash blow-ups of jet schemes},
     journal = {Annales de l'Institut Fourier},
     pages = {2577--2588},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {69},
     number = {6},
     year = {2019},
     doi = {10.5802/aif.3302},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2019__69_6_2577_0/}
}
de Fernex, Tommaso; Docampo, Roi. Nash blow-ups of jet schemes. Annales de l'Institut Fourier, Tome 69 (2019) no. 6, pp. 2577-2588. doi : 10.5802/aif.3302. https://aif.centre-mersenne.org/item/AIF_2019__69_6_2577_0/

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