Restricted tangent bundle of rational curves on projective hypersurfaces

Lucas Mioranci

Restricted tangent bundle of rational curves on projective hypersurfaces

Algebraic Geometry 2025-07-21 v1

Authors: Lucas Mioranci

Abstract

We determine all triples $(e,d,n)$ for which a general degree $d$ hypersurface $X\subset \mathbb{P}^n$ 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.

Keywords

restricted tangent bundle rational curves projective hypersurfaces balanced tangent bundle rational normal curve

Cite

@article{arxiv.2507.13927,
  title  = {Restricted tangent bundle of rational curves on projective hypersurfaces},
  author = {Lucas Mioranci},
  journal= {arXiv preprint arXiv:2507.13927},
  year   = {2025}
}

Comments

38 pages. Comments and suggestions are welcome

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