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arXiv:1106.0207 [math.AG]AbstractReferencesReviewsResources

Log canonical thresholds, F-pure thresholds, and non-standard extensions

Bhargav Bhatt, Daniel J. Hernandez, Lance E. Miller, Mircea Mustata

Published 2011-06-01Version 1

We present a new relation between an invariant of singularities in characteristic zero (the log canonical threshold) and an invariant of singularities defined via the Frobenius morphism in positive characteristic (the F-pure threshold). We show that the set of limit points of sequences of the form (c_p), where c_p is the F-pure threshold of an ideal on an n-dimensional smooth variety in characteristic p, coincides with the set of log canonical thresholds of ideals on n-dimensional smooth varieties in characteristic zero. We prove this by combining results of Hara and Yoshida with non-standard constructions.

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