Convex separably rationally connected complete intersections

Furukawa, Katsuhisa

doi:10.1090/proc/13159

Convex separably rationally connected complete intersections
HTML articles powered by AMS MathViewer

by Katsuhisa Furukawa PDF

Proc. Amer. Math. Soc. 144 (2016), 3657-3669 Request permission

Abstract:

We give a generalization of a result of R. Pandharipande to arbitrary characteristic: We prove that, if $X$ is a convex, separably rationally connected, smooth complete intersection in $\mathbb {P}^N$ over an algebraically closed field of arbitrary characteristic, then $X$ is rational homogeneous.

References

E. Arbarello, M. Cornalba, P. A. Griffiths, and J. Harris, Geometry of algebraic curves. Vol. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 267, Springer-Verlag, New York, 1985. MR 770932, DOI 10.1007/978-1-4757-5323-3
W. Barth and A. Van de Ven, Fano varieties of lines on hypersurfaces, Arch. Math. (Basel) 31 (1978/79), no. 1, 96–104. MR 510081, DOI 10.1007/BF01226420
Frédéric Campana and Thomas Peternell, Projective manifolds whose tangent bundles are numerically effective, Math. Ann. 289 (1991), no. 1, 169–187. MR 1087244, DOI 10.1007/BF01446566
Frédéric Campana and Thomas Peternell, $4$-folds with numerically effective tangent bundles and second Betti numbers greater than one, Manuscripta Math. 79 (1993), no. 3-4, 225–238. MR 1223018, DOI 10.1007/BF02568341
Olivier Debarre and Laurent Manivel, Sur la variété des espaces linéaires contenus dans une intersection complète, Math. Ann. 312 (1998), no. 3, 549–574 (French). MR 1654757, DOI 10.1007/s002080050235
Katsuhisa Furukawa, Rational curves on hypersurfaces, J. Reine Angew. Math. 665 (2012), 157–188. MR 2908742, DOI 10.1515/CRELLE.2011.114
Jun-Muk Hwang, Rigidity of rational homogeneous spaces, International Congress of Mathematicians. Vol. II, Eur. Math. Soc., Zürich, 2006, pp. 613–626. MR 2275613
A. Kanemitsu, Fano n-folds with nef tangent bundle and Picard number greater than n-5, Math. Z, to appear.
János Kollár, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 32, Springer-Verlag, Berlin, 1996. MR 1440180, DOI 10.1007/978-3-662-03276-3
Ngaiming Mok, On Fano manifolds with nef tangent bundles admitting 1-dimensional varieties of minimal rational tangents, Trans. Amer. Math. Soc. 354 (2002), no. 7, 2639–2658. MR 1895197, DOI 10.1090/S0002-9947-02-02953-7
R. Pandharipande, Convex rationally connected varieties, Proc. Amer. Math. Soc. 141 (2013), no. 5, 1539–1543. MR 3020841, DOI 10.1090/S0002-9939-2012-11429-7
Kiwamu Watanabe, Fano 5-folds with nef tangent bundles and Picard numbers greater than one, Math. Z. 276 (2014), no. 1-2, 39–49. MR 3150191, DOI 10.1007/s00209-013-1185-2