Vol. 6, No. 4, 2013

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Free and very free morphisms into a Fermat hypersurface

Tabes Bridges, Rankeya Datta, Joseph Eddy, Michael Newman and John Yu

Vol. 6 (2013), No. 4, 437–445
Abstract

This paper studies the existence of free and very free curves on the degree 5 Fermat hypersurface in 5 over an algebraically closed field of characteristic 2. We explicitly compute a free curve in degree 8, and a very free curve in degree 9. We also prove that free and very free curves cannot exist in lower degrees.

Keywords
free morphisms, very free morphisms, Fermat hypersurface, Fermat hypersurface over a field of characteristic 2
Mathematical Subject Classification 2010
Primary: 14-02
Secondary: 14M22
Milestones
Received: 5 August 2012
Revised: 6 November 2012
Accepted: 8 November 2012
Published: 8 October 2013

Communicated by Ravi Vakil
Authors
Tabes Bridges
Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
Chicago, IL 60607-7045
United States
Rankeya Datta
Department of Mathematics
University of Michigan
Ann Arbor, MI 48109
United States
Joseph Eddy
Department of Mathematics
Columbia University
New York, NY 10027
United States
Michael Newman
Department of Mathematics
University of Michigan
Ann Arbor, MI 48109
United States
John Yu
Department of Mathematics
Columbia University
New York, NY 10027
United States