## Some remarks on plane curves over fields of finite characteristic.(English)Zbl 0607.14023

Let X be a curve over an algebraically closed field K and let $$X^*$$ be its dual curve; that is the curve made up of associating to every smooth point its tangent line. Thus $$X^*$$ becomes equipped with a map $$\phi: X\to X^*.$$ If K has zero characteristic then it is a classical result that $$\phi$$ is birational. If K has characteristic $$p>0$$ then this result does not hold longer - those curves for which it does hold are called ”reflexive”. The paper under review is devoted to a general study of when a nonsingular curve is reflexive.
Reviewer: D.Goss

### MSC:

 14E05 Rational and birational maps 14G15 Finite ground fields in algebraic geometry

### Keywords:

reflexive curve; Weierstrass point; dual curve; characteristic p
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### References:

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