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function fields of algebraic surfaces

Journal of the Institute of Mathematics of Jussieu (1)

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1 results

HOMOGENEOUS SPACE FIBRATIONS OVER SURFACES
Part of
- Families, fibrations
Yi Zhu
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 18 / Issue 2 / March 2019

Published online by Cambridge University Press:

03 April 2017, pp. 293-327

Print publication:

March 2019
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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.