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Zbl 0756.14021
Kaji, Hajime
On the Gauss maps of space curves in characteristic $p$. II. (English)
[J] Compos. Math. 78, No.3, 261-269 (1991). ISSN 0010-437X; ISSN 1570-5846/e

[For part I see ibid. 70, No. 2, 177-197 (1989; Zbl 0692.14015).]\par Let $C$ be a smooth irreducible complete curve over an algebraically closed field of characteristic $p>0$. The author studies the Gauss map of a morphism $\iota$ of $C$ into a projective space when:\par (i) $C$ is elliptic and $\iota$ is unramified;\par (ii) $C$ has genus $g\ge 2$ and the sheaf of relative differentials has degree less than $2g-2$.\par For (i) the main new result is that when $C$ is ordinary the Gauss map gives rise to a cyclic étale cover of jacobians; for (ii) that the Gauss map has separable degree 1.
[G.Horrocks (Newcastle upon Tyne)]

MSC 2000:: *14H50 Space curves
14G15 Finite ground fields

Keywords: elliptic curve; Gauss map; sheaf of relative differentials; characteristic $p$

Citations: Zbl 0692.14015

Cited in: Zbl 0974.14037

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