A matrix equation on triangulated Riemann surfaces

作者：Yamaki Daisuke^*

来源：Proceedings of the Japan Academy Series A-Mathematical Sciences, 2014, 90(2): 37-42.

DOI：10.3792/pjaa.90.37

• Triangulated Riemann surface
• combinatorial Hodge theory
• associate matrix

In [1], Wilson defined holomorphic 1-cochains and combinatrial period matrices of triangulated Riemann surfaces by using the combinatorial Hodge star operator, introduced in [2]. In this paper, we define a matrix and call this matrix the associate matrix. Then, we prove that among the three matrices, which are a period matrix, a combinatorial period matrix which is introduced by Wilson [2] and an associate matrix, there exists a matrix equation. Then we also show that an associate matrix is an element of the Siegel upper half space, so this means that a trianguted Riemann surface gives three elements of the Siegel upper half space.

• 出版日期2014-2