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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.
This completes prior results by Knutsen, Lelli-Chiesa and Mongardi.
Original language | English |
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Pages (from-to) | 49-76 |
Number of pages | 22 |
Journal | Pure and applied mathematics quarterly |
Volume | 13 |
Issue number | 1 |
DOIs | |
Publication status | Published - 14 Sept 2018 |
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