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Miura conjecture on Affine curves

Shinji Miura gave certain multivariable polynomials that express an Affine curve for a given algebraic function field F and its degree one place O, if F contains such an O. Suppose the equations contain t ( 2) variables, and that the pole orders at O are for each i = 2, , t, by arranging a 1 , , a t , then we say that the orders a 1 , , a t are telescopic. On the other hand, the number t ¼ ( t 1) of the equations in the Miura canonical form is determined by a 1 , , a t . If t ¼ = t 1, then we

doi:10.18910/9751
fatcat:pfd72mywyfefhica2kze2zuvny