Normality of minimal log canonical centers of threefolds in mixed and positive characteristic
[Normalité des centres log-canoniques minimaux sur les variétés tri-dimensionnelles en caractéristique mixte et positive]
Arvidsson, Emelie1 ; Posva, Quentin2
1University of Utah, Department of Mathematics, JWB 311, 84112 Salt Lake City, Utah (USA)
2HHU, 25.13-03.33, 40225 Düsseldorf (Germany)
Annales de l'Institut Fourier, Online first, 33 p.

We prove the normality of minimal log canonical centers on threefold pairs whose residue fields are perfect of residue characteristics $p\ne 2,3 $ and $5$. We also show that the union of all log canonical centers on threefold pairs with standard coefficients are seminormal provided that the residue characteristics are large enough. In contrast, we provide an example of a non-seminormal log canonical center on a threefold in characteristic $3$, and give sufficient conditions to construct similar examples.

On prouve la normalité des centres log canoniques minimaux sur les paires de dimension trois dont les caractéristiques résiduelles sont différentes de $2,3$ et $5$. On montre également que l’union de tous les centres log canoniques sur les paires de dimension trois à coefficients standards est semi-normale dès que les caractéristiques résiduelles sont assez grandes. Par contraste, on décrit un exemple de centre log canonique non-semi-normal sur une variété tri-dimensionnelle en caractéristique $3$, et on donne des conditions suffisantes pour construire de tels exemples.

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DOI : 10.5802/aif.3780
Classification : 14G17, 14B05, 14J17, 14J30
Keywords: Positive and mixed characteristic, MMP, singularities, lc centers, threefolds
Mots-clés : caractéristique positive et mixte, MMP, singularités, centres lc, variétés tri-dimensionnelles

Arvidsson, Emelie  1   ; Posva, Quentin  2

1 University of Utah, Department of Mathematics, JWB 311, 84112 Salt Lake City, Utah (USA)
2 HHU, 25.13-03.33, 40225 Düsseldorf (Germany) 
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Arvidsson, Emelie; Posva, Quentin. Normality of minimal log canonical centers of threefolds in mixed and positive characteristic. Annales de l'Institut Fourier, Online first, 33 p.

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