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Weierstrass weights of fixed points of an involution

Published online by Cambridge University Press:  01 November 1997

Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1003, U.S.A. e-mail:


Let X be a curve with an involution T which fixes r points. We show that the Weierstrass weight of a fixed point is at least (r−2)(r−4)/8. Our proof is independent of the recent result of Torres.

We consider the case where X=Fn, the nth Fermat curve, and T is any of the involutions of Fn. We find that our bound is equal to the actual weight in all known cases (n[les ]7) and compute then n=8 case to demonstrate that the equality continues to hold.

Research Article
Cambridge Philosophical Society 1997

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