Proceedings of the Japan Academy, Series A, Mathematical Sciences

A matrix equation on triangulated Riemann surfaces

Daisuke Yamaki

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 30 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.pja/1391091381

Digital Object Identifier
doi:10.3792/pjaa.90.37

Mathematical Reviews number (MathSciNet)
MR3161544

Zentralblatt MATH identifier
1286.30033

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

Keywords
Triangulated Riemann surface combinatorial Hodge theory associate matrix

Citation

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. https://projecteuclid.org/euclid.pja/1391091381


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References

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