On the number of compatibly Frobenius split subvarieties, prime F -ideals, and log canonical centers

Karl Schwede[1]; Kevin Tucker[2]

  • [1] University of Michigan Department of Mathematics Ann Arbor, Michigan 48109 (USA)
  • [2] University of Michigan, Department of Mathematics, Ann Arbor, Michigan 48109

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 5, page 1515-1531
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Schwede, Karl, and Tucker, Kevin. "On the number of compatibly Frobenius split subvarieties, prime $F$-ideals, and log canonical centers." Annales de l’institut Fourier 60.5 (2010): 1515-1531. <http://eudml.org/doc/116312>.

@article{Schwede2010,
abstract = {Let $X$ be a projective Frobenius split variety with a fixed Frobenius splitting $\theta $. In this paper we give a sharp uniform bound on the number of subvarieties of $X$ which are compatibly Frobenius split with $\theta $. 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.},
affiliation = {University of Michigan Department of Mathematics Ann Arbor, Michigan 48109 (USA); University of Michigan, Department of Mathematics, Ann Arbor, Michigan 48109},
author = {Schwede, Karl, Tucker, Kevin},
journal = {Annales de l’institut Fourier},
keywords = {Frobenius split; compatibly Frobenius split subvariety; log canonical center; F-ideal; -ideal},
language = {eng},
number = {5},
pages = {1515-1531},
publisher = {Association des Annales de l’institut Fourier},
title = {On the number of compatibly Frobenius split subvarieties, prime $F$-ideals, and log canonical centers},
url = {http://eudml.org/doc/116312},
volume = {60},
year = {2010},
}

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
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 5
SP - 1515
EP - 1531
AB - Let $X$ be a projective Frobenius split variety with a fixed Frobenius splitting $\theta $. In this paper we give a sharp uniform bound on the number of subvarieties of $X$ which are compatibly Frobenius split with $\theta $. 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.
LA - eng
KW - Frobenius split; compatibly Frobenius split subvariety; log canonical center; F-ideal; -ideal
UR - http://eudml.org/doc/116312
ER -

References

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