Node Polynomials for Curves on Surfaces
We complete the proof of a theorem we announced and partly proved in [Math. Nachr. 271 (2004), 69-90, math.AG/0111299]. The theorem concerns a family of curves on a family of surfaces. It has two parts. The first was proved in that paper. It describes a natural cycle that enumerates the curves in th...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2022 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211728 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Node Polynomials for Curves on Surfaces. Steven Kleiman and Ragni Piene. SIGMA 18 (2022), 059, 23 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730846457298944 |
|---|---|
| author | Kleiman, Steven Piene, Ragni |
| author_facet | Kleiman, Steven Piene, Ragni |
| citation_txt | Node Polynomials for Curves on Surfaces. Steven Kleiman and Ragni Piene. SIGMA 18 (2022), 059, 23 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We complete the proof of a theorem we announced and partly proved in [Math. Nachr. 271 (2004), 69-90, math.AG/0111299]. The theorem concerns a family of curves on a family of surfaces. It has two parts. The first was proved in that paper. It describes a natural cycle that enumerates the curves in the family with precisely ordinary nodes. The second part is proved here. It asserts that, for ≤ 8, the class of this cycle is given by a computable universal polynomial in the pushdowns to the parameter space of products of the Chern classes of the family.
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| first_indexed | 2026-04-17T15:09:26Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211728 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T15:09:26Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kleiman, Steven Piene, Ragni 2026-01-09T12:53:31Z 2022 Node Polynomials for Curves on Surfaces. Steven Kleiman and Ragni Piene. SIGMA 18 (2022), 059, 23 pages 1815-0659 2020 Mathematics Subject Classification: 14N10; 14C20; 14H40; 14K05 arXiv:2202.11611 https://nasplib.isofts.kiev.ua/handle/123456789/211728 https://doi.org/10.3842/SIGMA.2022.059 We complete the proof of a theorem we announced and partly proved in [Math. Nachr. 271 (2004), 69-90, math.AG/0111299]. The theorem concerns a family of curves on a family of surfaces. It has two parts. The first was proved in that paper. It describes a natural cycle that enumerates the curves in the family with precisely ordinary nodes. The second part is proved here. It asserts that, for ≤ 8, the class of this cycle is given by a computable universal polynomial in the pushdowns to the parameter space of products of the Chern classes of the family. Thanks are due to the referee for pointing out our inadvertent change of notation from [15], which is discussed immediately after the proof of Proposition 5.2. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Node Polynomials for Curves on Surfaces Article published earlier |
| spellingShingle | Node Polynomials for Curves on Surfaces Kleiman, Steven Piene, Ragni |
| title | Node Polynomials for Curves on Surfaces |
| title_full | Node Polynomials for Curves on Surfaces |
| title_fullStr | Node Polynomials for Curves on Surfaces |
| title_full_unstemmed | Node Polynomials for Curves on Surfaces |
| title_short | Node Polynomials for Curves on Surfaces |
| title_sort | node polynomials for curves on surfaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211728 |
| work_keys_str_mv | AT kleimansteven nodepolynomialsforcurvesonsurfaces AT pieneragni nodepolynomialsforcurvesonsurfaces |