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On the Gauss maps of space curves in characteristic \(p\). II. (English) Zbl 0756.14021

[For part I see ibid. 70, No. 2, 177-197 (1989; Zbl 0692.14015).]
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:
(i) \(C\) is elliptic and \(\iota\) is unramified;
(ii) \(C\) has genus \(g\geq 2\) and the sheaf of relative differentials has degree less than \(2g-2\).
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.

MSC:

14H50 Plane and space curves
14G15 Finite ground fields in algebraic geometry

Citations:

Zbl 0692.14015
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References:

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