Restricted tangent bundle of rational curves on projective hypersurfaces

2025/07/18 by Mioranci, Lucas
#14H60 #14J45 #14J70 (Primary) 14G17 #14N25 #14Q15 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.13927

Abstract

We determine all triples (e,d,n) for which a general degree d hypersurface X⊂ ℙⁿ contains a degree e rational curve C with balanced restricted tangent bundle T_X|_C. In addition, we show how to compute explicit examples of hypersurfaces with balanced T_X|_C when C is a rational normal curve.

Citations

• Normal bundles of rational curves in Grassmannians
• Normal Bundles of Rational Normal Curves on Hypersurfaces
• Regular and rigid curves on some Calabi-Yau and general-type complete intersections
• Interpolation of curves on Fano hypersurfaces
• Interpolation of rational scrolls
• Vector bundles on trees of smooth rational curves
• Low-degree Rational curves on hypersurfaces in projective spaces and their degenerations
• Normal bundles of rational curves on complete intersections
• Normal bundles of lines on hypersurfaces
• Normal bundles of rational curves in projective space
• Quadratic solutions of quadratic forms
• Interpolation for normal bundles of general curves
• Irreducible Components of Hilbert Schemes of Rational Curves with given\n Normal Bundle
• Convex separably rationally connected complete intersections
• On plane rational curves and the splitting of the tangent bundle
• Normal bundles of rational curves in projective spaces

Related

• Normal Bundles of Rational Normal Curves on Hypersurfaces
• Rational curves on hypersurfaces of low degree, II
• Low-degree Rational curves on hypersurfaces in projective spaces and their degenerations
• Very free rational curves in Fano varieties
• Balanced rational curves and minimal rational connectedness of Fano hypersurfaces