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...

Повний опис

Збережено в:
Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2022
Автор: Oprea, Dragos
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2022
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/211726
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points. Dragos Oprea. SIGMA 18 (2022), 061, 21 pages

Репозитарії

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.
first_indexed 2026-03-21T04:20:49Z
format Article
fulltext
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