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Abstract <p> We prove that an affine cone <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8529_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(X\)</EquationSource> </InlineEquation> admits a surjective morphism from an affine space if and only if <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8529_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(X\)</EquationSource> </InlineEquation> is unirational. </p>

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Affine Cones as Images of Affine Spaces

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Ivan Arzhantsev

摘要

Abstract

We prove that an affine cone \(X\) admits a surjective morphism from an affine space if and only if \(X\) is unirational.