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

Abstract

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.

19 pages, AmS-TeX 2.1, report 2

Cited by in corpus (6)

• Projective varieties with many degenerate subvarieties
• Congruences of lines in ${\mathbb{P}}^5$, quadratic normality, and completely exceptional Monge-Ampère equations
• On a special class of smooth codimension two subvarieties in ${\mathbb{P}}^n$, $n\ge 5$
• On the lifting problem in ${\mathbb{P}}^4$ in characteristic $p$
• Weakly-exceptional singularities in higher dimensions
• Towards a Halphen theory of linear series on curves