Projects per year

## 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

This completes prior results by Knutsen, Lelli-Chiesa and Mongardi.

*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.

Original language | English |
---|---|

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 Sep 2018 |

## Fingerprint Dive into the research topics of 'Brill-Noether theory for curves on generic abelian surfaces'. Together they form a unique fingerprint.

## Projects

- 1 Finished