# zbMATH — the first resource for mathematics

Weierstrass gap sequences at points of curves on some rational surfaces. (English) Zbl 1372.14028
Summary: Let $$\tilde{C}$$ be a non-singular plane curve of degree $$d\geq 8$$ with an involution $$\sigma$$ over an algebraically closed field of characteristic 0 and $$\tilde{P}$$ a point of $$\tilde{C}$$ fixed by $$\sigma$$. Let $$\pi : \tilde{C}\rightarrow C = \tilde{C} / \langle\sigma\rangle$$ be the double covering. We set $$P = \pi (\tilde{P})$$. When the intersection multiplicity at $$\tilde{P}$$ of the curve $$\tilde{C}$$ and the tangent line at $$\tilde{P}$$ is equal to $$d - 3$$ or $$d - 4$$, we determine the Weierstrass gap sequence at $$P$$ on $$C$$ using blowing-ups and blowing-downs of some rational surfaces.
##### MSC:
 14H55 Riemann surfaces; Weierstrass points; gap sequences 14H50 Plane and space curves 14H30 Coverings of curves, fundamental group 14J26 Rational and ruled surfaces
Full Text: