On the number of compatibly Frobenius split subvarieties, prime F-ideals, and log canonical centers
Annales de l'Institut Fourier, Volume 60 (2010) no. 5, p. 1515-1531

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.

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.

DOI : https://doi.org/10.5802/aif.2563
Classification:  13A35,  14B05,  14J17
Keywords: Frobenius split, compatibly Frobenius split subvariety, log canonical center, F-ideal
@article{AIF_2010__60_5_1515_0,
     author = {Schwede, Karl and Tucker, Kevin},
     title = {On the number of compatibly Frobenius split subvarieties, prime $F$-ideals, and log canonical centers},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {60},
     number = {5},
     year = {2010},
     pages = {1515-1531},
     doi = {10.5802/aif.2563},
     mrnumber = {2766221},
     zbl = {1223.14009},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2010__60_5_1515_0}
}
Schwede, Karl; Tucker, Kevin. On the number of compatibly Frobenius split subvarieties, prime $F$-ideals, and log canonical centers. Annales de l'Institut Fourier, Volume 60 (2010) no. 5, pp. 1515-1531. doi : 10.5802/aif.2563. http://www.numdam.org/item/AIF_2010__60_5_1515_0/

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