Extending rationally connected fibrations from ample subvarieties

Using deformation theory of rational curves, we prove a conjecture of Sommese on the extendability of morphisms from ample subvarieties when the morphism is a smooth (or mildly singular) fibration with rationally connected fibers. We apply this result in the context of Fano fibrations and prove a cl...

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Bibliographic Details
Published in:Manuscripta mathematica 2022-09, Vol.169 (1-2), p.19-32
Main Authors: de Fernex, Tommaso, Lau, Chung Ching
Format: Article
Language:English
Subjects:
Algebraic Geometry
Calculus of Variations and Optimal Control
Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
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Summary:Using deformation theory of rational curves, we prove a conjecture of Sommese on the extendability of morphisms from ample subvarieties when the morphism is a smooth (or mildly singular) fibration with rationally connected fibers. We apply this result in the context of Fano fibrations and prove a classification theorem for projective bundle and quadric fibration structures on ample subvarieties.
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-021-01319-1