Let φ:Σ1⟶P2\documentclass[12pt]{minimal}
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\begin{document}$$\varphi :\Sigma _1\longrightarrow {\mathbb {P}}^2$$\end{document} be a blow up at a point on P2\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {P}}^2$$\end{document}. Let C be the proper transform of a smooth plane curve of degree d≥4\documentclass[12pt]{minimal}
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\begin{document}$$d\ge 4$$\end{document} by φ\documentclass[12pt]{minimal}
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\begin{document}$$\varphi $$\end{document}, and let P be a point on C. Let π:C~⟶C\documentclass[12pt]{minimal}
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\begin{document}$$\pi :{\tilde{C}}\longrightarrow C$$\end{document} be a double covering branched along the reduced divisor on C obtained as the intersection of C and a reduced divisor in |-2KΣ1|\documentclass[12pt]{minimal}
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\begin{document}$$|-2K_{\Sigma _1}|$$\end{document} containing P. In this paper, we investigate the Weierstrass semigroup H(P~)\documentclass[12pt]{minimal}
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\begin{document}$$H({\tilde{P}})$$\end{document} at the ramification point P~\documentclass[12pt]{minimal}
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\begin{document}$${\tilde{P}}$$\end{document} of π\documentclass[12pt]{minimal}
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\begin{document}$$\pi $$\end{document} over P, in the case where the intersection multiplicity at φ(P)\documentclass[12pt]{minimal}
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\begin{document}$$\varphi (P)$$\end{document} of φ(C)\documentclass[12pt]{minimal}
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\begin{document}$$\varphi (C)$$\end{document} and the tangent line at φ(P)\documentclass[12pt]{minimal}
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\begin{document}$$\varphi (P)$$\end{document} of φ(C)\documentclass[12pt]{minimal}
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\begin{document}$$\varphi (C)$$\end{document} is d-1\documentclass[12pt]{minimal}
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\begin{document}$$d-1$$\end{document}.
