NDLI: Fibrations by curves with more than one nonsmooth point

Content Provider	Springer Nature Link
Author	Salomão, Rodrigo
Copyright Year	2014
Abstract	Bertini’s theorem on variable singular pointsmay fail in positive characteristic, as was discovered by Zariski in 1944. In fact, he found fibrations by nonsmooth curves. In this work we continue to classify this phenomenon in characteristic three by constructing the first example, rising in the literature, of fibrations with more than one nonsmooth point. Our approach has been motivated by the close relation between it and the theory of regular but nonsmooth curves, or equivalently, nonconservative function fields in one variable. In analogy to the Kodaira-Néron classification of special fibers of minimal fibrations by elliptic curves, we also construct the minimal proper regular model of some fibrations by nonsmooth projective plane quartic curves and determine the structure of the bad fibers.
Ending Page	292
Page Count	26
Starting Page	267
File Format	PDF
ISSN	16787544
e-ISSN	16787714
Journal	Bulletin of the Brazilian Mathematical Society
Issue Number	2
Volume Number	45
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-06-07
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Plane and space curves Theoretical, Mathematical and Computational Physics Algebraic functions; function fields Mathematics Fibrations, degenerations relative Frobenius morphism nonconservative function fields Families, moduli (algebraic) regular but nonsmooth curves Singularities, local rings minimal models Bertini’s theorem fibrations by nonsmooth curves
Content Type	Text
Resource Type	Article
Subject	Mathematics

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