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Revista Matemática Complutense

, Volume 29, Issue 2, pp 423–437 | Cite as

Uniform families of minimal rational curves on Fano manifolds

  • Gianluca OcchettaEmail author
  • Luis E. Solá Conde
  • Kiwamu Watanabe
Article
  • 142 Downloads

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.

Keywords

Fano manifolds Homogeneity VMRT Dual varieties 

Mathematics Subject Classification

Primary 14J45 Secondary 14M17 14M22 

Notes

Acknowledgments

The results in this paper were obtained mostly while the second author was a Visiting Researcher at the Korea Institute for Advanced Study (KIAS) and the Department of Mathematics of the University of Warsaw. He would like to thank both institutions for their support and hospitality. The authors would like to thank J. Wiśniewski for his interesting comments and discussions on this topic, and an anonymous referee, whose remarks helped to improve substantially the final form of this paper.

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Copyright information

© Universidad Complutense de Madrid 2015

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TrentoPovo di TrentoItaly
  2. 2.Course of Mathematics, Programs in Mathematics, Electronics and Informatics, Graduate School of Science and EngineeringSaitama UniversitySaitamaJapan

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