an:06137826
Zbl 1372.14028
Komeda, Jiryo; Ohbuchi, Akira
Weierstrass gap sequences at points of curves on some rational surfaces
EN
Tsukuba J. Math. 36, No. 2, 217-233 (2012).
00314649
2012
j
14H55 14H50 14H30 14J26
Weierstrass gap sequence; Weierstrass semigroup; smooth plane curve; double covering of a curve; blowing-up of a rational surface
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.