The order of speciality of an ample invertible sheaf L on a curve is the least integer m so that L ›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 for- mulate Castelnuovo's genus bound involving the order of speciality.
The principal result of the present work consists in the proof that an intersection of quadrics passing through a canonical curve is a reduced variety. The possible cases when the intersection of quadrics does not coincide with the curve itself are also examined in this article. Figures: 1. Bibliography: 8 references.
It is proved that special flows over irrational rotations and under functions whose Fourier coefficients are of order O(1/| n |) are disjoint in the sense of Furstenberg from all mixing flows. This is an essential strengthening of a classical result by Kocergin on the absence of mixing of special flows built over irrational rotations and under bounded variation roof functions.