Abstract
Let X be a smooth curve of genus g > 0. For any \({n \geq 2}\) and any n distinct points \({P_{1}, . . . ,P_{n} \in X, \,\,{\rm let}\,\, H(P_1, . . . ,P_n)}\) be the set of all \({(a_{1}, . . . ,a_{n}) \in \mathbb{N}^n {\rm such}\,{\rm that}\,\, \mathcal{O}_{X}(a_{1}P_{1} + \cdots + a_{n}P_{n})}\) is spanned. We raise some questions on the minimal number of generators of the semigroup \({H(P_{1}, . . . ,P_{n})}\) and test it in a few cases.
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The author was partially supported by MIUR and GNSAGA of INdAM (Italy).
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Ballico, E. On the Weierstrass semigroups of n points of a smooth curve. Arch. Math. 104, 207–215 (2015). https://doi.org/10.1007/s00013-015-0740-y
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DOI: https://doi.org/10.1007/s00013-015-0740-y