Low rank orthogonal bundles and quadric fibrations
Peer reviewed, Journal article
Published version
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https://hdl.handle.net/11250/3106123Utgivelsesdato
2023Metadata
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Originalversjon
Journal of the Korean Mathematical Society. 2023, 60 (6), 1137-1169. 10.4134/JKMS.j220125Sammendrag
Let C be a curve and V → C an orthogonal vector bundle of rank r. For r ≤ 6, the structure of V can be described using ten- sor, symmetric and exterior products of bundles of lower rank, essentially due to the existence of exceptional isomorphisms between Spin(r, C) and other groups for these r. We analyze these structures in detail, and in particular use them to describe moduli spaces of orthogonal bundles. Fur- thermore, the locus of isotropic vectors in V defines a quadric subfibration QV ⊂ PV . Using familiar results on quadrics of low dimension, we exhibit isomorphisms between isotropic Quot schemes of V and certain ordinary Quot schemes of line subbundles. In particular, for r ≤ 6 this gives a method for enumerating the isotropic subbundles of maximal degree of a general V , when there are finitely many.