Proceedings of the Japan Academy, Series A, Mathematical Sciences

A matrix equation on triangulated Riemann surfaces

Daisuke Yamaki

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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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Proc. Japan Acad. Ser. A Math. Sci., Volume 90, Number 2 (2014), 37-42.

First available in Project Euclid: 30 January 2014

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Primary: 30F99: None of the above, but in this section

Triangulated Riemann surface combinatorial Hodge theory associate matrix


Yamaki, Daisuke. A matrix equation on triangulated Riemann surfaces. Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 2, 37--42. doi:10.3792/pjaa.90.37.

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