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<p>The paper presents an analog of an old result by the author and V.&#xa0;Voevodsky, according to which a&#xa0;Riemann surface admits a&#xa0;conformal structure defined by an equilateral triangulation if and only if the corresponding algebraic curve can be defined over the field of algebraic numbers; a&#xa0;similar result is obtained for the square-tiled surfaces.</p>

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SQUARE-TILED SURFACES AND CURVES OVER NUMBER FIELDS

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • George B. Shabat

摘要

The paper presents an analog of an old result by the author and V. Voevodsky, according to which a Riemann surface admits a conformal structure defined by an equilateral triangulation if and only if the corresponding algebraic curve can be defined over the field of algebraic numbers; a similar result is obtained for the square-tiled surfaces.