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Abstract <p> We construct a new class of affine complements <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8540_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb P^M\setminus S\)</EquationSource> </InlineEquation> with trivial automorphism group, where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8540_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">\(S\subset\mathbb P^M\)</EquationSource> </InlineEquation> is a rational hypersurface, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8540_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(M\)</EquationSource> </InlineEquation> is odd, and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8540_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(M\geq 5\)</EquationSource> </InlineEquation>. </p>

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Affine Complements in the Projective Space with Trivial Automorphism Group

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  • 发表日期：

    2025年6月1日

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  • A. V. Pukhlikov

摘要

Abstract

We construct a new class of affine complements \(\mathbb P^M\setminus S\) with trivial automorphism group, where \(S\subset\mathbb P^M\) is a rational hypersurface, \(M\) is odd, and \(M\geq 5\) .