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Locating Divisors on Zariski Surfaces
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Let k be an algebraically closed field of characteristic p≠0 and Xg⊂A3k be a normal surface defined by an equation of the form zp=g(x, y). Let Fg be the field extension of the prime subfield generated by the coefficients of g and assume the number of singularities of Xg is the maximum possible, which is generally the case. This paper describes a finite algebraic extension Lg of Fg such that Lg[x, y, z] contains a basis of the group of Weil divisors of Xg.
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