Let be a projective Frobenius split variety with a fixed Frobenius splitting . In this paper we give a sharp uniform bound on the number of subvarieties of which are compatibly Frobenius split with . Similarly, we give a bound on the number of prime -ideals of an -finite -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 une variété projective Frobenius scindée avec un scindage de Frobenius . Dans cet article nous donnons une borne optimale et uniforme sur le nombre de sous-variétés de qui sont compatibles avec le scindage de Frobenius . De même, nous donnons une borne sur le nombre de -idéaux d’un anneau local -fini -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.
Keywords: Frobenius split, compatibly Frobenius split subvariety, log canonical center, F-ideal
Mot clés : Frobenius scindé, compatiblement Frobenius scindé sous-variété, centres canoniques logarithmiques, F-idéaux
Schwede, Karl 1; Tucker, Kevin 2
@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}, pages = {1515--1531}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {5}, year = {2010}, doi = {10.5802/aif.2563}, mrnumber = {2766221}, zbl = {1223.14009}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2563/} }
TY - JOUR AU - Schwede, Karl AU - Tucker, Kevin TI - On the number of compatibly Frobenius split subvarieties, prime $F$-ideals, and log canonical centers JO - Annales de l'Institut Fourier PY - 2010 SP - 1515 EP - 1531 VL - 60 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2563/ DO - 10.5802/aif.2563 LA - en ID - AIF_2010__60_5_1515_0 ER -
%0 Journal Article %A Schwede, Karl %A Tucker, Kevin %T On the number of compatibly Frobenius split subvarieties, prime $F$-ideals, and log canonical centers %J Annales de l'Institut Fourier %D 2010 %P 1515-1531 %V 60 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2563/ %R 10.5802/aif.2563 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.2563/
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