Orthogonal Bundles and Skew-Hamiltonian Matrices

Abuaf, Roland ; Boralevi, Ada

Canadian journal of mathematics, Tome 67 (2015) no. 5, pp. 961-989

Résumé

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.

Détail

DOI : 10.4153/CJM-2014-034-9

Mots-clés : 14J60, 15B99, orthogonal vector bundles, moduli spaces, skew-Hamiltonian matrices

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