On the order of speciality of a simple, special, and complete linear system on a curve

Edoardo Ballico; Masaaki Homma; Akira Ohbuchi

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2002; 39(4): 593-609

Printed July 1, 2002

On the order of speciality of a simple, special, and complete linear system on a curve

Edoardo Ballico, Masaaki Homma, and Akira Ohbuchi

University of Trento, Kanagawa University, Tokushima University

Abstract

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Abstract

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.

Keywords: order of speciality, Castelnuovo's genus bound

MSC numbers: Primary 14H51; Secondary 14H45, 14J26