Irreducible Contact Curves via Graph Stratification
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909275465449472 |
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| author | Muratore, Giosuè |
| author_facet | Muratore, Giosuè |
| contents | We prove that the moduli space of contact stable maps to $\mathbb{P}^{2n+1}$ of degree $d$ admits a stratification parameterized by graphs. We use it to determine the number of irreducible rational contact curves in $\mathbb{P}^{2n+1}$ with any Schubert condition. We give explicitely some of these invariants for $\mathbb{P}^{3}$ and $\mathbb{P}^{5}$. We give another proof of the formula for the number of plane contact curves in $\mathbb{P}^{3}$ meeting the appropriate number of lines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_01477 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Irreducible Contact Curves via Graph Stratification Muratore, Giosuè Algebraic Geometry 14N10, 14C17, 53D10 (Primary) 14H10, 14D22, 14L30 (Secondary) We prove that the moduli space of contact stable maps to $\mathbb{P}^{2n+1}$ of degree $d$ admits a stratification parameterized by graphs. We use it to determine the number of irreducible rational contact curves in $\mathbb{P}^{2n+1}$ with any Schubert condition. We give explicitely some of these invariants for $\mathbb{P}^{3}$ and $\mathbb{P}^{5}$. We give another proof of the formula for the number of plane contact curves in $\mathbb{P}^{3}$ meeting the appropriate number of lines. |
| title | Irreducible Contact Curves via Graph Stratification |
| topic | Algebraic Geometry 14N10, 14C17, 53D10 (Primary) 14H10, 14D22, 14L30 (Secondary) |
| url | https://arxiv.org/abs/2209.01477 |