Tsukuba Journal of Mathematics

Weierstrass gap sequences at points of curves on some rational surfaces

Jiryo Komeda and Akira Ohbuchi

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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

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

First available in Project Euclid: 21 January 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H55: Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx] 14H50: Plane and space curves 14H30: Coverings, fundamental group [See also 14E20, 14F35] 14J26: Rational and ruled surfaces

Weierstrass gap sequence Weierstrass semigroup Smooth plane curve Double covering of a curve Blowing-up of a rational surface


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

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