Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points
We study tautological vector bundles over the Hilbert scheme of points on surfaces. For each -trivial surface, we write down a simple criterion ensuring that the tautological bundles are big and nef, and illustrate it by examples. In the 3 case, we extend recent constructions and results of Bini, Bo...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2022 |
| ISSN: | 1815-0659 |
| Main Author: | |
| 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/123456789/211726 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points. Dragos Oprea. SIGMA 18 (2022), 061, 21 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862722108722774016 |
|---|---|
| author | Oprea, Dragos |
| author_facet | Oprea, Dragos |
| citation_txt | Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points. Dragos Oprea. SIGMA 18 (2022), 061, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study tautological vector bundles over the Hilbert scheme of points on surfaces. For each -trivial surface, we write down a simple criterion ensuring that the tautological bundles are big and nef, and illustrate it by examples. In the 3 case, we extend recent constructions and results of Bini, Boissière, and Flamini from the Hilbert scheme of 2 and 3 points to an arbitrary number of points. Among the -trivial surfaces, the case of Enriques surfaces is the most involved. Our techniques apply to other smooth projective surfaces, including blowups of 3s and minimal surfaces of general type, as well as to the punctual Quot schemes of curves.
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| first_indexed | 2026-03-21T04:20:49Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211726 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T04:20:49Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Oprea, Dragos 2026-01-09T12:53:12Z 2022 Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points. Dragos Oprea. SIGMA 18 (2022), 061, 21 pages 1815-0659 2020 Mathematics Subject Classification: 14C05; 14D20; 14C17 arXiv:2208.06599 https://nasplib.isofts.kiev.ua/handle/123456789/211726 https://doi.org/10.3842/SIGMA.2022.061 We study tautological vector bundles over the Hilbert scheme of points on surfaces. For each -trivial surface, we write down a simple criterion ensuring that the tautological bundles are big and nef, and illustrate it by examples. In the 3 case, we extend recent constructions and results of Bini, Boissière, and Flamini from the Hilbert scheme of 2 and 3 points to an arbitrary number of points. Among the -trivial surfaces, the case of Enriques surfaces is the most involved. Our techniques apply to other smooth projective surfaces, including blowups of 3s and minimal surfaces of general type, as well as to the punctual Quot schemes of curves. We are grateful to G. Bini, S. Boissiere, and F. Flamini for correspondence related to [7]; their paper served as motivation for this work. We thank A. Marian and R. Pandharipande for collaboration that led to [25, 26, 27, 33]. We thank the referees for their careful reading of the manuscript and for their comments. The author is supported by NSF grant DMS1802228. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points Article published earlier |
| spellingShingle | Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points Oprea, Dragos |
| title | Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points |
| title_full | Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points |
| title_fullStr | Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points |
| title_full_unstemmed | Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points |
| title_short | Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points |
| title_sort | big and nef tautological vector bundles over the hilbert scheme of points |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211726 |
| work_keys_str_mv | AT opreadragos bigandneftautologicalvectorbundlesoverthehilbertschemeofpoints |