on the expected dimension of brill–noether loci of stable rank-2 vector bundles with fixed determinant

This paper investigates the brill–noether loci b2k,l of stable rank–2 vector bundles with fixed determinant over a smooth projective curve c. focusing on the case k = 1, explicit families of stable bundles are constructed using extension theory, and it is shown that these families have the expected brill–noether dimension. this provides a concrete and constructive realization of the expected components of b21,l, complementing classical petri map results for line bundles and recent developments in non-abelian brill–noether theory.