Open Access
February 2014 A matrix equation on triangulated Riemann surfaces
Daisuke Yamaki
Proc. Japan Acad. Ser. A Math. Sci. 90(2): 37-42 (February 2014). DOI: 10.3792/pjaa.90.37


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.


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Daisuke Yamaki. "A matrix equation on triangulated Riemann surfaces." Proc. Japan Acad. Ser. A Math. Sci. 90 (2) 37 - 42, February 2014.


Published: February 2014
First available in Project Euclid: 30 January 2014

zbMATH: 1286.30033
MathSciNet: MR3161544
Digital Object Identifier: 10.3792/pjaa.90.37

Primary: 30F99

Keywords: associate matrix , combinatorial Hodge theory , Triangulated Riemann surface

Rights: Copyright © 2014 The Japan Academy

Vol.90 • No. 2 • February 2014
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