Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CJM
Abstract view

# Orthogonal Bundles and Skew-Hamiltonian Matrices

Published:2015-07-21
Printed: Oct 2015
• Roland Abuaf,
Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK
Using properties of skew-Hamiltonian matrices and classic connectedness results, we prove that the moduli space $M_{ort}^0(r,n)$ of stable rank $r$ orthogonal vector bundles on $\mathbb{P}^2$, with Chern classes $(c_1,c_2)=(0,n)$, and trivial splitting on the general line, is smooth irreducible of dimension $(r-2)n-\binom{r}{2}$ for $r=n$ and $n \ge 4$, and $r=n-1$ and $n\ge 8$. We speculate that the result holds in greater generality.