On a fibre bundle version of the Caporaso-Harris formula
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929429085683712 |
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| author | Biswas, Indranil Choudhury, Apratim Das, Nilkantha Mukherjee, Ritwik |
| author_facet | Biswas, Indranil Choudhury, Apratim Das, Nilkantha Mukherjee, Ritwik |
| contents | The Caporaso-Harris formula gives a recursive algorithm to enumerate delta nodal degree d curves in P^2. The recursion is obtained in terms of curves of lower degree that are tangent to a given divisor. This paper presents two generalizations of this method. The first result is on enumeration of one cuspidal curves on P^2, and the second result is an extension to the fiber bundle setting. We solve the question of counting the characteristic number planar nodal cubics in P^3 by extending the idea of Caporaso-Harris. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14832 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a fibre bundle version of the Caporaso-Harris formula Biswas, Indranil Choudhury, Apratim Das, Nilkantha Mukherjee, Ritwik Algebraic Geometry 14N35, 14J45 The Caporaso-Harris formula gives a recursive algorithm to enumerate delta nodal degree d curves in P^2. The recursion is obtained in terms of curves of lower degree that are tangent to a given divisor. This paper presents two generalizations of this method. The first result is on enumeration of one cuspidal curves on P^2, and the second result is an extension to the fiber bundle setting. We solve the question of counting the characteristic number planar nodal cubics in P^3 by extending the idea of Caporaso-Harris. |
| title | On a fibre bundle version of the Caporaso-Harris formula |
| topic | Algebraic Geometry 14N35, 14J45 |
| url | https://arxiv.org/abs/2407.14832 |