Differential-geometric methods for the lifting problem and linear systems on plane curves

Details Differential-geometric methods for the lifting problem and linear systems on plane curves Differential-geometric methods for the lifting problem and linear systems on plane curves

1993-09-23

arxiv.org/abs/alg-geom/9309005v1

Mathematics

Algebraic Geometry

19 pages, AmS-TeX 2.1, report 2

Scientific paper

Let $X$ be an integral projective variety of codimension two, degree $d$ and dimension $r$ and $Y$ be its general hyperplane section. The problem of lifting generators of minimal degree $\sigma$ from the homogeneous ideal of $Y$ to the homogeneous ideal of $X$ is studied. A conjecture is given in terms of $d$, $r$ and $\sigma$; it is proved in the cases $r=1,2,3$. A description is given of linear systems on smooth plane curves whose dimension is almost maximal.

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