Orthogonal Bundles and Skew-Hamiltonian Matrices
Canadian journal of mathematics, Tome 67 (2015) no. 5, pp. 961-989
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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.
Mots-clés :
14J60, 15B99, orthogonal vector bundles, moduli spaces, skew-Hamiltonian matrices
Abuaf, Roland; Boralevi, Ada. Orthogonal Bundles and Skew-Hamiltonian Matrices. Canadian journal of mathematics, Tome 67 (2015) no. 5, pp. 961-989. doi: 10.4153/CJM-2014-034-9
@article{10_4153_CJM_2014_034_9,
author = {Abuaf, Roland and Boralevi, Ada},
title = {Orthogonal {Bundles} and {Skew-Hamiltonian} {Matrices}},
journal = {Canadian journal of mathematics},
pages = {961--989},
year = {2015},
volume = {67},
number = {5},
doi = {10.4153/CJM-2014-034-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2014-034-9/}
}
TY - JOUR AU - Abuaf, Roland AU - Boralevi, Ada TI - Orthogonal Bundles and Skew-Hamiltonian Matrices JO - Canadian journal of mathematics PY - 2015 SP - 961 EP - 989 VL - 67 IS - 5 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2014-034-9/ DO - 10.4153/CJM-2014-034-9 ID - 10_4153_CJM_2014_034_9 ER -
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