Ordinary varieties with trivial canonical bundle are not uniruled

We prove that smooth, projective, K-trivial, weakly ordinary varieties over a perfect field of characteristic [Formula: see text] are not geometrically uniruled. We also show a singular version of our theorem, which is sharp in multiple aspects. Our work, together with Langer’s results, implies that...

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Autores principales: Patakfalvi, Zsolt, Zdanowicz, Maciej
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550111/
https://www.ncbi.nlm.nih.gov/pubmed/34720195
http://dx.doi.org/10.1007/s00208-021-02165-y
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author Patakfalvi, Zsolt
Zdanowicz, Maciej
author_facet Patakfalvi, Zsolt
Zdanowicz, Maciej
author_sort Patakfalvi, Zsolt
collection PubMed
description We prove that smooth, projective, K-trivial, weakly ordinary varieties over a perfect field of characteristic [Formula: see text] are not geometrically uniruled. We also show a singular version of our theorem, which is sharp in multiple aspects. Our work, together with Langer’s results, implies that varieties of the above type have strongly semistable tangent bundles with respect to every polarization.
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spelling pubmed-85501112021-10-29 Ordinary varieties with trivial canonical bundle are not uniruled Patakfalvi, Zsolt Zdanowicz, Maciej Math Ann Article We prove that smooth, projective, K-trivial, weakly ordinary varieties over a perfect field of characteristic [Formula: see text] are not geometrically uniruled. We also show a singular version of our theorem, which is sharp in multiple aspects. Our work, together with Langer’s results, implies that varieties of the above type have strongly semistable tangent bundles with respect to every polarization. Springer Berlin Heidelberg 2021-06-09 2021 /pmc/articles/PMC8550111/ /pubmed/34720195 http://dx.doi.org/10.1007/s00208-021-02165-y Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Patakfalvi, Zsolt
Zdanowicz, Maciej
Ordinary varieties with trivial canonical bundle are not uniruled
title Ordinary varieties with trivial canonical bundle are not uniruled
title_full Ordinary varieties with trivial canonical bundle are not uniruled
title_fullStr Ordinary varieties with trivial canonical bundle are not uniruled
title_full_unstemmed Ordinary varieties with trivial canonical bundle are not uniruled
title_short Ordinary varieties with trivial canonical bundle are not uniruled
title_sort ordinary varieties with trivial canonical bundle are not uniruled
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550111/
https://www.ncbi.nlm.nih.gov/pubmed/34720195
http://dx.doi.org/10.1007/s00208-021-02165-y
work_keys_str_mv AT patakfalvizsolt ordinaryvarietieswithtrivialcanonicalbundlearenotuniruled
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