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HOMOGENEOUS SPACE FIBRATIONS OVER SURFACES

Part of: Families, fibrations

Published online by Cambridge University Press:  03 April 2017

Yi Zhu
Yi Zhu*
Affiliation:
Pure Mathematics, University of Waterloo, Waterloo, ON N2L3G1, Canada ([email protected])
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Abstract

By studying the theory of rational curves, we introduce a notion of rational simple connectedness for projective homogeneous spaces. As an application, we prove that over a function field of an algebraic surface over an algebraically closed field, a variety whose geometric generic fiber is a projective homogeneous space admits a rational point if and only if the elementary obstruction vanishes.

Keywords

rationally simply connected varietiesprojective homogeneous spacesrational pointsfunction fields of algebraic surfaces

MSC classification

Primary: 14D06: Fibrations, degenerations
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 18 , Issue 2 , March 2019 , pp. 293 - 327
Copyright
© Cambridge University Press 2017 

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