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- Title
On extensions of a double covering of plane curves and Weierstrass semigroups of the double covering type.
- Authors
Komeda, Jiryo; Watanabe, Kenta
- Abstract
Let $$C$$ be a smooth plane curve of degree $$d, P$$ be a point on $$C$$ , and let $$\pi :\tilde{C}\rightarrow C$$ be a double covering of the curve $$C$$ with the branch point $$P$$ . In this paper, we give a best possible sufficient condition for the double covering $$\pi $$ to extend to a double covering $$\tilde{\pi }:X\rightarrow {\mathbb {P}}^{2}$$ branched along a reduced divisor of degree six which intersects transversally the curve $$C$$ at smooth $$6d$$ points containing $$P$$ .
- Subjects
PLANE curves; WEIERSTRASS semigroups; SMOOTHNESS of functions; DIVISOR theory; COVERING spaces (Topology)
- Publication
Semigroup Forum, 2015, Vol 91, Issue 2, p517
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-015-9718-0