Automorphism Groups of Plane Curves

Abstract

We study the automorphism and collineation groups of plane curves, i.e., in ℙ², that are not necessarily smooth, and obtain bounds for these curves in terms of, their degree and the number of singularities. We also introduce the notion of bad curves and good curves, and show that all bad curves are rational.

Key Words:

• Automorphisms
• Collineations
• Plane curves
• Singularities
• Simplex

Mathematics Subject Classification:

• Primary 14Hxx
• Secondary 14H37
• 14H20
• 14H50

Acknowledgments

The first author would like to thank Alan Howard for all the help he received as his student. This work forms a part of his thesis. The second author would like to acknowledge a partial grant from the Faculty Development Fund at UM-Flint. We would also like to sincerely thank the referee for the careful reading of the manuscript, and for the many suggestions.

Notes

^#Communicated by K. Misra.

^†To Arleen and Marianne.