Postulation of lines in P3 revisited

TL;DR

This paper offers a new proof for the well-known result that general lines in projective spaces have good postulation, using specialization to a hyperplane, and extends the approach to study codimension 2 linear subspaces.

Contribution

It provides a novel proof technique for postulation of lines and extends the method to higher codimension linear subspaces in projective spaces.

Findings

New proof of good postulation for general lines in projective spaces

Extension of proof technique to codimension 2 linear subspaces

Potential for further studies using specialization methods

Abstract

The purpose of the present note is to provide a new proof ot the well-known result due to Hartshorne and Hirschowitz to the effect that general lines in projective spaces have good postulation. Our approach uses specialization to a hyperplane and thus opens door to study postulation of general codimension 2 linear subspaces in projective spaces.