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Abstract <p> We consider a real del Pezzo surface without points. We prove that the same surface over the complex number field <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8531_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb C\)</EquationSource> </InlineEquation> has Picard number at least <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8531_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(2\)</EquationSource> </InlineEquation>. </p>

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Real del Pezzo Surfaces without Points

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Grigory Belousov

摘要

Abstract

We consider a real del Pezzo surface without points. We prove that the same surface over the complex number field \(\mathbb C\) has Picard number at least \(2\) .