论文标题
关于Hurwitz问题和锥形球形指标的注释
A note on the Hurwitz problem and cone spherical metrics
论文作者
论文摘要
我们是由圆锥球形指标激励着阳性属的紧凑riemann表面，以解决Hurwitz问题的特殊情况。确切地说，让$ d，\，g $和$ \ ell $是三个正整数，$λ$是以下$（\ ell+2）$分区的$（\ ell+2）$分区， b_q),\,(m_1+1,1,\cdots,1),\cdots, (m_{\ell}+1,1,\cdots,1),\] where $(m_1,\cdots, m_{\ell})$ is a partition of $p+q-2+2g$, we prove that there exists a branched cover from some compact Riemann surface of属$ g $ to riemann sphere $ {\ bbb p}^1 $带有分支数据$λ$。前两位作者发现了零属属的类似物（{\ it代数colloq。} {\ bf 27}（2020），第2、231-246号），这些指标在$ {\ bbb p}^1 $上刺激了此类指标，并在其中构思了上述陈述。
We are motivated by cone spherical metrics on compact Riemann surfaces of positive genus to solve a special case of the Hurwitz problem. Precisely speaking, letting $d,\,g$ and $\ell$ be three positive integers and $Λ$ be the following collection of $(\ell+2)$ partitions of a positive integer $d$: \[(a_1,\cdots, a_p),\,(b_1,\cdots, b_q),\,(m_1+1,1,\cdots,1),\cdots, (m_{\ell}+1,1,\cdots,1),\] where $(m_1,\cdots, m_{\ell})$ is a partition of $p+q-2+2g$, we prove that there exists a branched cover from some compact Riemann surface of genus $g$ to the Riemann sphere ${\Bbb P}^1$ with branch data $Λ$. An analogue for the genus-zero case was found by the first two authors ({\it Algebra Colloq.} {\bf 27} (2020), no. 2, 231-246), who were stimulated by such metrics on ${\Bbb P}^1$ and conjectured the veracity of the above statement there.
