On certain N--sheeted coverings and numerical semigroups which cannot be realized as Weierstrass semigroups
| dc.creator | Torres, Fernando | |
| dc.date | 1994-07-26 | |
| dc.date | 1995-03-06 | |
| dc.date.accessioned | 2026-07-07T08:57:53Z | |
| dc.date.available | 2026-07-07T08:57:53Z | |
| dc.description | A curve $X$ is said to be of type $(N,γ)$ if it is an $N$--sheeted covering of a curve of genus $γ$ with at least one totally ramified point. A numerical semigroup $H$ is said to be of type $(N,γ)$ if it has $γ$ positive multiples of $N$ in $[N,2Nγ]$ such that its $γ^{th}$ element is $2Nγ$ and $(2γ+1)N \in H$. If the genus of $X$ is large enough and $N$ is prime, $X$ is of type $(N,γ)$ if and only if there is a point $P \in X$ such that the Weierstrass semigroup at $P$ is of type $(N,γ)$ (this generalizes the case of double coverings of curves). Using the proof of this result and the Buchweitz's semigroup, we can construct numerical semigroups that cannot be realized as Weierstrass semigroups although they might satisfy Buchweitz's criterion. | |
| dc.description | ICTP preprint, 18 pages, Latex v. 2.1. Reason for resubmission: (1) I reformulated the principal result (Theorem A) in order to obtain a better bound on the genus for the results concerning semigroups. Remarks 3.11 contains examples that show the sharpness (or the necessity of the hypothesis) of most of the result stated in the paper | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9407012 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9407012 | |
| dc.identifier | Com. Alg. 23(11) (1995) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147106 | |
| dc.subject | Algebraic Geometry | |
| dc.title | On certain N--sheeted coverings and numerical semigroups which cannot be realized as Weierstrass semigroups | |
| dc.type | text |