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Orthogonal Bundles and Skew-Hamiltonian Matrices

Published online by Cambridge University Press:  20 November 2018

Roland Abuaf  and
Ada Boralevi
Roland Abuaf
Affiliation:
Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK. e-mail: r.abuaf@imperial.ac.uk
Ada Boralevi
Affiliation:
Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy. e-mail: ada.boralevi@sissa.it
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Abstract

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Using properties of skew-Hamiltonian matrices and classic connectedness results, we prove that the moduli space $M_{\text{ort}}^{0}\left( r,\,n \right)$ of stable rank $r$ orthogonal vector bundles on ${{\mathbb{P}}^{2}}$ , with Chern classes $\left( {{c}_{1}},\,{{c}_{2}} \right)\,=\,\left( 0,\,n \right)$ and trivial splitting on the general line, is smooth irreducible of dimension $\left( r-2 \right)n\,-\,\left( _{2}^{r} \right)$ for $r\,=\,n$ and $n\,\ge \,4$ , and $r\,=\,n-1$ and $n\,\ge \,8$ . We speculate that the result holds in greater generality.

Keywords

14J6015B99orthogonal vector bundlesmoduli spacesskew-Hamiltonian matrices

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 5 , 01 October 2015 , pp. 961 - 989
Copyright
Copyright © Canadian Mathematical Society 2015

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