Free and Very Free Morphisms into a Fermat Hypersurface
Tabes Bridges, Rankeya Datta, Joseph Eddy, Michael Newman, John Yu
TL;DR
This paper investigates the existence of free and very free rational curves on a degree 5 Fermat hypersurface in projective 5-space over characteristic 2, identifying specific degrees where such curves exist.
Contribution
It establishes the degrees in which free and very free curves exist on the Fermat hypersurface, providing new existence results in positive characteristic.
Findings
Free and very free curves exist in degrees 8 and 9.
No such curves exist in degrees lower than 8.
Results are specific to characteristic 2.
Abstract
This paper studies the existence of free and very free curves on the degree 5 Fermat hypersurface in P^5 over a field of characteristic 2. We find that such curves exist in degrees 8 and 9 and not in lower degrees.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · French Historical and Cultural Studies · Geometric Analysis and Curvature Flows