Planarizations and maps taking lines to linear webs of conics

TL;DR

This paper explores generalizations of Moebius's theorem by studying maps that transform line segments into plane curves and conics from specific linear systems, broadening understanding of geometric transformations.

Contribution

It introduces new classes of maps that extend classical line-to-curve transformations to include conics within linear systems, expanding geometric mapping theory.

Findings

Maps can transform line intervals into various plane curves.

Certain maps can send line intervals to conics in linear systems.

The work generalizes classical theorems to broader geometric contexts.

Abstract

Aiming at a generalization of a classical theorem of Moebius, we study maps that take line intervals to plane curves, and also maps that take line intervals to conics from certain linear systems.