#### Vol. 6, No. 4, 2013

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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 ${ℙ}^{5}$ 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
Primary: 14-02
Secondary: 14M22