non-abelian brill–noether loci of stable rank-2 bundles with fixed determinant: the case k = 2

This paper studies the brill–noether loci b22,l of stable rank–2 vector bundles with fixed determinant l on a smooth projective curve c. building on the classical petri map results for line bundles and teixidor’s injectivity theorem for rank–2 bundles with canonical determinant, explicit families of stable bundles with two independent global sections are constructed using extension theory. it is shown that these families have the expected brill–noether dimension and fit naturally into the general framework of non-abelian brill–noether theory developed by mukai and others.