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
Main Author: Oprea, Dragos
Format: Article
Language:English
Published: Інститут математики НАН України 2022
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
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Summary: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.
ISSN:1815-0659