## Tsukuba Journal of Mathematics

### Weierstrass gap sequences at points of curves on some rational surfaces

#### 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.

#### Article information

Source
Tsukuba J. Math., Volume 36, Number 2 (2013), 217-233.

Dates
First available in Project Euclid: 21 January 2013

https://projecteuclid.org/euclid.tkbjm/1358777000

Digital Object Identifier
doi:10.21099/tkbjm/1358777000

Mathematical Reviews number (MathSciNet)
MR3058240

Zentralblatt MATH identifier
1372.14028

#### Citation

Komeda, Jiryo; Ohbuchi, Akira. Weierstrass gap sequences at points of curves on some rational surfaces. Tsukuba J. Math. 36 (2013), no. 2, 217--233. doi:10.21099/tkbjm/1358777000. https://projecteuclid.org/euclid.tkbjm/1358777000