Geodesic
A NOTE ON RANK TWO STABLE BUNDLES OVER SURFACES
Glasgow mathematical journal, Tome 64 (2022) no. 2, pp. 397-410

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DOI

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. 
REYES-AHUMADA, GRACIELA; ROA-LEGUIZAMÓN, L.; TORRES-LÓPEZ, H. A NOTE ON RANK TWO STABLE BUNDLES OVER SURFACES. Glasgow mathematical journal, Tome 64 (2022) no. 2, pp. 397-410. doi: 10.1017/S0017089521000185
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     title = {A {NOTE} {ON} {RANK} {TWO} {STABLE} {BUNDLES} {OVER} {SURFACES}},
     journal = {Glasgow mathematical journal},
     pages = {397--410},
     year = {2022},
     volume = {64},
     number = {2},
     doi = {10.1017/S0017089521000185},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089521000185/}
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