Very stable bundles and properness of the Hitchin map View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-02-27

AUTHORS

Christian Pauly, Ana Peón-Nieto

ABSTRACT

Let X be a smooth complex projective curve of genus g≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g\ge 2$$\end{document} and let K be its canonical bundle. In this note we show that a stable vector bundle E on X is very stable, i.e. E has no non-zero nilpotent Higgs field, if and only if the restriction of the Hitchin map to the vector space of Higgs fields H0(X,End(E)⊗K)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^0(X, \mathrm {End}(E) \otimes K)$$\end{document} is a proper map. More... »

PAGES

143-148

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10711-018-0333-6

DOI

http://dx.doi.org/10.1007/s10711-018-0333-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1101237454


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