TY - JOUR
T1 - Brill-Noether theory for curves on generic abelian surfaces
AU - Bayer, Arend
AU - Li, Chunyi
PY - 2018/9/14
Y1 - 2018/9/14
N2 - 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.
AB - 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.
U2 - 10.4310/PAMQ.2017.v13.n1.a2
DO - 10.4310/PAMQ.2017.v13.n1.a2
M3 - Article
VL - 13
SP - 49
EP - 76
JO - Pure and applied mathematics quarterly
JF - Pure and applied mathematics quarterly
SN - 1558-8599
IS - 1
ER -