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arXiv · 2011.10567

Extending rationally connected fibrations from ample subvarieties

Tommaso de Fernex·Chung Ching Lau
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Abstract

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.

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Tommaso de Fernex, Chung Ching Lau. 2020-11-18. Extending rationally connected fibrations from ample subvarieties. https://arxiv.org/abs/2011.10567

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