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On the order of speciality of a simple, special, and complete linear system on a curve. (English) Zbl 1058.14503
Summary: The order of speciality of an ample invertible sheaf $$L$$ on a curve is the least integer $$m$$ so that $$L^{\otimes m}$$ is nonspecial. There is a reasonable upper bound of the order of speciality for a simple invertible sheaf in terms of its degree and projective dimension. We study the case where it reaches the upper bound. Moreover, we formulate Castelnuovo’s genus bound involving the order of speciality.
##### MSC:
 14H51 Special divisors on curves (gonality, Brill-Noether theory) 14H45 Special algebraic curves and curves of low genus
##### Keywords:
Castelnuovo’s genus bound
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