First, we give some Weierstrass semigroups which cannot be attained by any smooth curve on a smooth compact toric surface. Next, for any integer $l\ge 2$ 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 $n\le 10$ 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.

首先，我们给出一些Weierstrass半群，这些群不能由光滑紧致复曲面上的任何光滑曲线获得。接下来，对于任何整数$升\ge \mathrm{2个}$我们描述了度投影线的环状覆盖物的总衍生物点的维尔斯特拉斯半群升使用$升-\mathrm{1个}$非负整数。最后，我们将研究位于圆环T作用下的光滑紧凑的复曲面S上的平滑曲线C，圆环T是S的密集开放子集。对于偶数整数$ñ\le 10$我们表征了循环覆盖度为n的总分枝点的Weierstrass半群，这是S的复曲面纤维对C的限制，使得分枝点位于某个T不变除数上。