Normal bundles of rational curves on complete intersections

2017/05/23 by Coskun, Izzet, Riedl, Eric · 3 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.08441

Abstract

Let X ⊂ ℙⁿ be a general Fano complete intersection of type (d₁,…, d_k). If at least one d_i is greater than 2, we show that X contains rational curves of degree e ≤ n with balanced normal bundle. If all d_i are 2 and n≥ 2k+1, we show that X contains rational curves of degree e ≤ n-1 with balanced normal bundle. As an application, we prove a stronger version of the theorem of Z. Tian \citeTian, Q. Chen and Y. Zhu \citeChenZhu that X is separably rationally connected by exhibiting very free rational curves in X of optimal degrees.

Cited by

• Separable rational connectedness and k-plane sections of hypersurfaces
• Restricted tangent bundle of rational curves on projective hypersurfaces
• The Harder-Narasimhan Filtration of a Trigonal Canonical Curve

Related

• Very free rational curves in Fano varieties
• Regular and rigid curves on some Calabi-Yau and general-type complete intersections
• Rational curves on complete intersections in positive characteristic
• Normal Bundles of Rational Normal Curves on Hypersurfaces
• Balanced rational curves and minimal rational connectedness of Fano hypersurfaces