Homogeneous Fibrations over Curves
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homogeneousrationalcurvesprojectiveadmitsalgebraicapplicationconnectedness
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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, a projective homogeneous space admits a rational point if the elementary obstruction vanishes.
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