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<p>For each even integer <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2130_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(k \ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, we construct an explicit real two-dimensional family <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2130_Article_IEq2.gif" Format="GIF" Height="27" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^{(k)}_{r,\theta }\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>C</mi> <mrow> <mi>r</mi> <mo>,</mo> <mi>θ</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mrow> </msubsup> </math></EquationSource> </InlineEquation> of non-hyperelliptic pseudo-real Riemann surfaces of genus <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2130_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="135" /> </InlineMediaObject> <EquationSource Format="TEX">\(g=1+(2k-3)k^{4}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mi>k</mi> <mo>-</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> <msup> <mi>k</mi> <mn>4</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>. For each of them, we compute its field of moduli and also a minimal field of definition.</p>

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Explicit computation of the field of moduli of some non-hyperelliptic pseudo-real curves

  • 期刊论文

  • 发表日期：

    2025年5月7日

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  • Rubén A. Hidalgo

摘要

For each even integer \(k \ge 2\) k ≥ 2 , we construct an explicit real two-dimensional family \(C^{(k)}_{r,\theta }\) C r , θ ( k ) of non-hyperelliptic pseudo-real Riemann surfaces of genus \(g=1+(2k-3)k^{4}\) g = 1 + ( 2 k - 3 ) k 4 . For each of them, we compute its field of moduli and also a minimal field of definition.