Weierstrass n-semigroups with even n and curves on toric surfaces
Weierstrass n-semigroups with even n and curves on toric surfaces
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具有偶数 n 和复曲面上的曲线的 Weierstrass n 半群
DOI：
10.1016/j.jpaa.2021.106759
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发表时间：
2021
影响因子：
0.8
通讯作者：
Jiryo Komeda
中科院分区：
文献类型：
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作者：
Jiryo Komeda;Jiryo Komeda
首先，我们给出了光滑紧复曲面上的任意光滑曲线都不能得到的Weierstrass半群。其次，对于任意整数l≥ 2，我们用l− 1个非负整数描述了l次射影线的循环覆盖的全分歧点的Weierstrass半群。最后，我们将研究光滑紧致复曲面S上的光滑曲线C，S上的稠密开子集环面T作用于光滑曲线C上。对n≤ 10的偶数，刻画了n次循环覆盖的全分歧点的Weierstrass半群，该覆盖是S的复曲面纤维化对C的限制，使得分歧点落在某个T-不变因子上.
First, we give some Weierstrass semigroups which cannot be attained by any smooth curve on a smooth compact toric surface. Next, for any integer l≥ 2 we describe the Weierstrass semigroup of a total ramification point of a cyclic covering of the projective line with degree l using l− 1 non-negative integers. And finally, we will study smooth curves C lying on a smooth compact toric surface S acted by the torus T which is a dense open subset of S. For an even integer n≤ 10 we characterize the Weierstrass semigroup of a total ramification point of a cyclic covering of degree n which is the restriction to C of a toric fibration of S such that the ramification point lies on some T-invariant divisor.