ABSTRACT
For a nonspecial line bundle ℒ on a smooth curve X we consider a presentation ℒ≃𝒦X−D+E which is minimal with respect to deg E. If ℒ is very ample, then this minimality means that any n-points of φℒ(X) with n≤deg E−1 are in general position while φℒ(E) spans a (deg E−2)-plane. In this work, we investigate conditions on D and E for ℒ≃𝒦X−D+E to be minimal. We also observe s-secant (s−k−1)-planes which are minimal with respect to the secant degree s for a given k. We apply minimal presentations to problems about the exactness of Green-Lazarsfeld’s conjecture on property (Np).
Acknowledgment
The author thanks KIAS for warm hospitality when she was an associate member in KIAS.