Archivio Istituzionale della RicercaUsing properties of skew-Hamiltonian matrices and classic connectedness results, we prove that the moduli space M0 (r, n) of stable rank r orthogonal vector bundles on P^2, with Chern classes (c1 , c2 ) = (0, n) and trivial splitting on the general line, is smooth irreducible of dimension (r-2) - {r choose 2} for r=n and n > 3 and r=n-1 and r>7. We speculate that the result holds in greater generality.
Orthogonal bundles and skew-Hamiltonian matrices / Abuaf, R; Boralevi, Ada. - In: CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES. - ISSN 0008-414X. - 67:5(2015), pp. 961-989. [10.4153/CJM-2014-034-9]
Orthogonal bundles and skew-Hamiltonian matrices
BORALEVI, ADA
2015
Abstract
Using properties of skew-Hamiltonian matrices and classic connectedness results, we prove that the moduli space M0 (r, n) of stable rank r orthogonal vector bundles on P^2, with Chern classes (c1 , c2 ) = (0, n) and trivial splitting on the general line, is smooth irreducible of dimension (r-2) - {r choose 2} for r=n and n > 3 and r=n-1 and r>7. We speculate that the result holds in greater generality.
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https://hdl.handle.net/11583/2674270
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