Susan Jane Colley, Gary Kennedy, “Cartan Prolongation of a Family of Curves Acquiring a Node”, SIGMA, 2018, Volume 14,031, 16 pp.

Cartan Prolongation of a Family of Curves Acquiring a Node

Susan Jane Colley^a, 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

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.

Keywords: curve families; nodal singularity; vector distributions; prolongation.

MSC: 58A30; 53A55; 58K50; 14D06; 14H99

Received: October 27, 2017; in final form April 3, 2018; Published online April 7, 2018

Language: English

DOI: 10.3842/SIGMA.2018.031