A Recursive Formula for Osculating Curves
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866914896215539712 |
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| author | Muratore, Giosuè |
| author_facet | Muratore, Giosuè |
| contents | Let $X$ be a smooth complex projective variety. Using a construction devised to 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 inflexion (asymptotic) lines for surfaces in $\mathbb{P}^{3}$ of Salmon, as well as Darboux's $27$ osculating conics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_00096 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A Recursive Formula for Osculating Curves Muratore, Giosuè Algebraic Geometry Primary 14N10, Secondary 14N15, 14N35 Let $X$ be a smooth complex projective variety. Using a construction devised to 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 inflexion (asymptotic) lines for surfaces in $\mathbb{P}^{3}$ of Salmon, as well as Darboux's $27$ osculating conics. |
| title | A Recursive Formula for Osculating Curves |
| topic | Algebraic Geometry Primary 14N10, Secondary 14N15, 14N35 |
| url | https://arxiv.org/abs/2003.00096 |