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A BOUND ON EMBEDDING DIMENSIONS OF GEOMETRIC GENERIC FIBERS

Part of: Families, fibrations Surfaces and higher-dimensional varieties Local theory

Published online by Cambridge University Press:  20 January 2016

ZACHARY MADDOCK
ZACHARY MADDOCK*
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095, USA; maddockz@math.ucla.edu

Abstract

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The author finds a limit on the singularities that arise in geometric generic fibers of morphisms between smooth varieties of positive characteristic by studying changes in embedding dimension under inseparable field extensions. This result is then used in the context of the minimal model program to rule out the existence of smooth varieties fibered by certain nonnormal del Pezzo surfaces over bases of small dimension.

MSC classification

Primary: 14B05: Singularities
Secondary: 14D99: None of the above, but in this section 14J17: Singularities
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 4 , 2016 , e3
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author 2016

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