@article{1434933662d442218d07ec4fd50bba57, title = "Brill-Noether theory for curves on generic abelian surfaces", abstract = "We completely describe the Brill-Noether theory for curves in the primitive linear system on generic abelian surfaces, in the following sense: given integers d and r, consider the variety V r d (|H|) parametrizing curves C in the primitive linear system |H| together with a torsion-free sheaf on C of degree d and r+1 global sections. We give a necessary and sufficient condition for this variety to be non-empty, and show that it is either a disjoint union of Grassmannians, or irreducible. Moreover, we show that, when non-empty, it is of expected dimension. This completes prior results by Knutsen, Lelli-Chiesa and Mongardi.", author = "Arend Bayer and Chunyi Li", year = "2018", month = "9", day = "14", doi = "10.4310/PAMQ.2017.v13.n1.a2", language = "English", volume = "13", pages = "49--76", journal = "Pure and applied mathematics quarterly", issn = "1558-8599", publisher = "International Press of Boston, Inc.", number = "1", }