THE Cab CURVE
نویسنده
چکیده
We characterize the defining equation of a plane algebraic curve with exactly one rational place Q at infinity, then give a basis of L(mQ) with pairwise distinct pole orders at Q. The defining equation can be regarded as a generalization of the Weierstrass form of a hyperelliptic curve. In this informal note I give an English proof of the results of the Cab curve found by Miura [4, 5, 6]. Throughout in this note, K denotes a perfect field, and a,b denote relatively prime positive integers. For a place Q of an algebraic function field, we define
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