Cartan Prolongation of a Family of Curves Acquiring a Node
Susan Jane Colley, Gary Kennedy
TL;DR
This paper investigates the structure of the Cartan prolongation of a family of plane curves with a nodal central member, using the monster/Semple tower construction to understand their geometric properties.
Contribution
It introduces a novel application of the monster/Semple tower to analyze the Cartan prolongation of curves with nodes, providing new insights into their geometric structure.
Findings
Detailed description of the Cartan prolongation structure
Identification of key geometric features of the family of curves
Extension of the monster/Semple tower methodology to nodal curves
Abstract
Using the monster/Semple tower construction, we study the structure of the Cartan prolongation of the family of plane curves with nodal central member.
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