Weierstrass weights of fixed points of an involution
Published online by Cambridge University Press: 01 November 1997
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
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 3 , November 1997 , pp. 385 - 392
- Cambridge Philosophical Society 1997