On the number of compatibly Frobenius split subvarieties, prime F-ideals, and log canonical centers
[Sur le nombre de sous-variétés compatiblement scindées par Frobenius, le nombre de F-idéaux premiers, et le nombre de centres canoniques logarithmiques]
Annales de l'Institut Fourier, Tome 60 (2010) no. 5, pp. 1515-1531.

Soit X une variété projective Frobenius scindée avec un scindage de Frobenius θ. Dans cet article nous donnons une borne optimale et uniforme sur le nombre de sous-variétés de X qui sont compatibles avec le scindage de Frobenius θ. De même, nous donnons une borne sur le nombre de F-idéaux d’un anneau local F-fini F-pur. Enfin, nous donnons également une borne sur le nombre de centres canoniques logarithmiques d’un paire canonique logarithmique. Cette dernière variante étend un cas particulier d’un résultat de Helmke.

Let X be a projective Frobenius split variety with a fixed Frobenius splitting θ. In this paper we give a sharp uniform bound on the number of subvarieties of X which are compatibly Frobenius split with θ. Similarly, we give a bound on the number of prime F-ideals of an F-finite F-pure local ring. Finally, we also give a bound on the number of log canonical centers of a log canonical pair. This final variant extends a special case of a result of Helmke.

DOI : https://doi.org/10.5802/aif.2563
Classification : 13A35,  14B05,  14J17
Mots clés : Frobenius scindé, compatiblement Frobenius scindé sous-variété, centres canoniques logarithmiques, F-idéaux
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Schwede, Karl; Tucker, Kevin. On the number of compatibly Frobenius split subvarieties, prime $F$-ideals, and log canonical centers. Annales de l'Institut Fourier, Tome 60 (2010) no. 5, pp. 1515-1531. doi : 10.5802/aif.2563. http://archive.numdam.org/articles/10.5802/aif.2563/

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