|
Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points
Dragos Oprea Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, USA
Аннотация:
We study tautological vector bundles over the Hilbert scheme of points on surfaces. For each $K$-trivial surface, we write down a simple criterion ensuring that the tautological bundles are big and nef, and illustrate it by examples. In the $K3$ 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 $K$-trivial surfaces, the case of Enriques surfaces is the most involved. Our techniques apply to other smooth projective surfaces, including blowups of $K3$s and minimal surfaces of general type, as well as to the punctual Quot schemes of curves.
Ключевые слова:
Hilbert scheme, Quot scheme, tautological bundles.
Поступила: 31 января 2022 г.; в окончательном варианте 31 июля 2022 г.; опубликована 12 августа 2022 г.
Образец цитирования:
Dragos Oprea, “Big and Nef Tautological Vector Bundles over the Hilbert Scheme of Points”, SIGMA, 18 (2022), 061, 21 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1857 https://www.mathnet.ru/rus/sigma/v18/p61
|
Статистика просмотров: |
Страница аннотации: | 45 | PDF полного текста: | 40 | Список литературы: | 11 |
|