Lines on hypersurfaces

TL;DR

This paper investigates the infinitesimal variation of lines on low degree hypersurfaces in projective space, describing the governing PDE system explicitly.

Contribution

It provides a detailed analysis of the differential equations controlling line variations on hypersurfaces, offering new insights into their geometric behavior.

Findings

Explicit PDE system for line variation

Characterization of infinitesimal deformations

Insights into hypersurface geometry

Abstract

This is a detailed study of the infinitesimal variation of the variety of lines through a point of a low degree hypersurface in pro jective space. The motion is governed by a system of partial differential equations which we describe explicitly.