Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 14 (2018), 031, 16 pages      arXiv:1710.02863      https://doi.org/10.3842/SIGMA.2018.031

Cartan Prolongation of a Family of Curves Acquiring a Node

Susan Jane Colley a and Gary Kennedy b
a) Department of Mathematics, Oberlin College, Oberlin, Ohio 44074, USA
b) Ohio State University at Mansfield, 1760 University Drive, Mansfield, Ohio 44906, USA

Received October 27, 2017, in final form April 03, 2018; Published online April 07, 2018

Abstract
Using the monster/Semple tower construction, we study the structure of the Cartan prolongation of the family $x_1x_2 = t$ of plane curves with nodal central member.

Key words: curve families; nodal singularity; vector distributions; prolongation.

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