Uniform families of minimal rational curves on Fano manifolds

DOI10.1007/S13163-015-0183-9zbMATH Open1338.14043arXiv1503.05312OpenAlexW2964048802MaRDI QIDQ282969

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Publication date: 13 May 2016

Published in: (Search for Journal in Brave)

Abstract: It is a well-known fact that families of minimal rational curves on rational homogeneous manifolds of Picard number one are uniform, in the sense that the tangent bundle to the manifold has the same splitting type on each curve of the family. In this note we prove that certain --stronger-- uniformity conditions on a family of minimal rational curves on a Fano manifold of Picard number one allow to prove that the manifold is homogeneous.

Full work available at URL: https://arxiv.org/abs/1503.05312

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