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- Title
A NOTE ON RANK TWO STABLE BUNDLES OVER SURFACES.
- Authors
REYES-AHUMADA, GRACIELA; ROA-LEGUIZAMÓN, L.; TORRES-LÓPEZ, H.
- Abstract
Let π : X → C be a fibration with integral fibers over a curve C and consider a polarization H on the surface X. Let E be a stable vector bundle of rank 2 on C. We prove that the pullback π*(E) is a H-stable bundle over X. This result allows us to relate the corresponding moduli spaces of stable bundles $${{\mathcal M}_C}(2,d)$$ and $${{\mathcal M}_{X,H}}(2,df,0)$$ through an injective morphism. We study the induced morphism at the level of Brill–Noether loci to construct examples of Brill–Noether loci on fibered surfaces. Results concerning the emptiness of Brill–Noether loci follow as a consequence of a generalization of Clifford's Theorem for rank two bundles on surfaces.
- Subjects
VECTOR bundles; GENERALIZATION
- Publication
Glasgow Mathematical Journal, 2022, Vol 64, Issue 2, p397
- ISSN
0017-0895
- Publication type
Article
- DOI
10.1017/S0017089521000185