Weierstrass semigroups satisfying the MP equalities and curves on toric surfaces
Weierstrass semigroups satisfying the MP equalities and curves on toric surfaces
复制标题
满足 MP 等式和复曲面上的曲线的 Weierstrass 半群
DOI：
10.1007/s00574-019-00145-0
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Ryo Kawaguchi and Jiryo Komeda
中科院分区：
文献类型：
--
作者：
Yuri Fedorov;Jiryo Komeda;Shigeki Matsutani;Emma Previato and Kazuhiko Aomoto;Jiryo Komeda and Shigeki Matsutani;Jiryo Komeda;Jiryo Komeda and Makiko Mase;Seon Jeong Kim and Jiryo Komeda;Jiryo Komeda;Ryo Kawaguchi and Jiryo Komeda
称一个数值半群是循环的，如果它是射影线的某个循环覆盖的全分歧点的Weierstrass半群。在这种情况下，H的标准基的元素满足数值条件，我们已经选择长期MP等式，后莫里森和Pinkham谁首先证明了他们。匡威则不成立，因为存在满足MP等式的半群不是循环的。本文考虑光滑紧复曲面S上的光滑曲线被S的稠密开子集环面T所作用的情形。证明了S的复曲面纤维化的C的限制的全分歧点的Weierstrass半群是循环的当且仅当它满足MP等式。
A numerical semigroupHis said to becyclicif it is the Weierstrass semigroup of a total ramification point of some cyclic covering of the projective line. In this case, the elements of the standard basis ofHsatisfy numerical conditions that we have chosen to term MP equalities, after Morrison and Pinkham who first proved them. The converse is not true, as there are semigroups satisfying the MP equalities that are not cyclic. In this paper, we consider the situation of a smooth curveClying on a smooth compact toric surfaceSacted on by the torusTwhich is a dense open subset ofS. We prove that the Weierstrass semigroup of a total ramification point of the restriction toCof a toric fibration ofS, which lies on someT-invariant divisor, is cyclic if and only if it satisfies the MP equalities.