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Separable rational connectedness and stability

Tian, Zhiyu (2015) Separable rational connectedness and stability. In: Rational Points, Rational Curves, and Entire Holomorphic Curves on Projective Varieties. Contemporary Mathematics. No.654. American Mathematical Society , Providence, RI, pp. 155-159. ISBN 978-1-4704-1458-0.

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In this short note we prove that in many cases the failure of a variety to be separably rationally connected is caused by the instability of the tangent sheaf (if there are no other obvious reasons). A simple application of the results proves that a smooth Fano complete intersection is separably rationally connected if and only if it is separably uniruled. In particular, a general such Fano complete intersection is separably rationally connected.

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Additional Information:© 2015 American Mathematical Society. The idea of the paper comes from a lecture on foliations in the summer school “rational points, rational curves, and entire holomorphic curves on projective varieties”. I would like to thank the organizers for their hard work and the all the lecturers in the summer school for their enlightening lectures. Finally, I would like to thank Prof. Olivier Debarre for suggesting the reference [Ben13]. This paper is dedicated to my dearest friend, Neipu, for his accompany in the time of happiness and in the time of sorrow, and for his strong belief in wait and hope. May he rest in peace.
Series Name:Contemporary Mathematics
Issue or Number:654
Record Number:CaltechAUTHORS:20160225-125522505
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64762
Deposited By: Tony Diaz
Deposited On:25 Feb 2016 22:53
Last Modified:03 Oct 2019 09:40

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