Free and Very Free Morphisms into a Fermat Hypersurface

Bridges, Tabes; Datta, Rankeya; Eddy, Joseph; Newman, M. F.; Yu, John‐Paul J.

doi:10.48550/arxiv.1207.5015

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2012

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“…The above theorem shows that on this X very free rational curves can only exist in degrees 5, 9, 10 and all e ≥ 13. In the recent paper [1], the authors showed that there is no very free rational curve in degree 5 and they explicitly gave a very free rational curve of degree 9. Definition 1.9.…”

Section: Introductionmentioning

confidence: 99%

Rational curves on Fermat hypersurfaces

Shen

2012

Comptes Rendus. Mathématique

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In this note we study rational curves on degree p r + 1 Fermat hypersurface in P p r +1 k , where k is an algebraically closed field of characteristic p.The key point is that the presence of Frobenius morphism makes the behavior of rational curves to be very different from that of charateristic 0. We show that if there exists N 0 such that for all e ≥ N 0 there is a degree e very free rational curve on X, then N 0 > p r (p r − 1).

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Section: Introductionmentioning

confidence: 99%

Rational curves on Fermat hypersurfaces

Shen

2012

Comptes Rendus. Mathématique

View full text Add to dashboard Cite

show abstract

Free and Very Free Morphisms into a Fermat Hypersurface

Cited by 1 publication

References 2 publications

Rational curves on Fermat hypersurfaces

Rational curves on Fermat hypersurfaces

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