Abstract
Let $\tilde{C}$ be a non-singular plane curve of degree d ≥ 8 with an involution σ over an algebraically closed field of characteristic 0 and $\tilde{P}$ a point of $\tilde{C}$ fixed by σ. Let π : $\tilde{C}$ → C = $\tilde{C}$/$/\langle\sigma\rangle $be the double covering. We set P = π($\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.
Citation
Jiryo Komeda. Akira Ohbuchi. "Weierstrass gap sequences at points of curves on some rational surfaces." Tsukuba J. Math. 36 (2) 217 - 233, December 2012. https://doi.org/10.21099/tkbjm/1358777000
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