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A recursive formula for osculating curves

Giosuè Muratore Department of Mathematics, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil

Algebraic Geometry mathscidoc:2203.45002

Arkiv for Matematik, 59, (1), 195-211, 2021.5
Let X be a smooth complex projective variety. Using a construction devised by Gathmann, we present a recursive formula for some of the Gromov–Witten invariants of X. We prove that, when X is homogeneous, this formula gives the number of osculating rational curves at a general point of a general hypersurface of X. This generalizes the classical well known pairs of inflection (asymptotic) lines for surfaces in P^3 of Salmon, as well as Darboux’s 27 osculating conics.
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@inproceedings{giosuè2021a,
  title={A recursive formula for osculating curves},
  author={Giosuè Muratore},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311104531480964957},
  booktitle={Arkiv for Matematik},
  volume={59},
  number={1},
  pages={195-211},
  year={2021},
}
Giosuè Muratore. A recursive formula for osculating curves. 2021. Vol. 59. In Arkiv for Matematik. pp.195-211. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311104531480964957.
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