# Geometry and Arithmetic

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#### DOI: 10.4171/119-1/4

Brill–Noether loci of stable rank-two vector bundles on a general curve

Ciro Ciliberto[1] and Flaminio Flamini[2]

(1) Università di Roma, Italy
(2) Università di Roma Tor Vergata, Italy

In this note we give an easy proof of the existence of generically smooth components of the expected dimension of certain Brill–Noether loci of stable rank 2 vector bundles on a curve with general moduli, with related applications to the Hilbert scheme of scrolls.

Keywords: Brill–Noether theory of vector bundles, Hilbert schemes of scrolls, moduli