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Abstract <p>We study a class of smooth projective <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8350_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(3\)</EquationSource> <!--LobJMat2560810Karzhemanov-m1--> </InlineEquation>-folds admitting wild automorphisms and relate this subject with smooth complete families of Fano varieties. Using isotriviality of some of the latter families we show that certain triples <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8350_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">\((X,f,\sigma)\)</EquationSource> <!--LobJMat2560810Karzhemanov-m2--> </InlineEquation> do not exist, where <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8350_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(X\)</EquationSource> <!--LobJMat2560810Karzhemanov-m3--> </InlineEquation> is a smooth projective <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8350_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(3\)</EquationSource> <!--LobJMat2560810Karzhemanov-m4--> </InlineEquation>-fold, <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8350_Article_IEq5.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma\)</EquationSource> <!--LobJMat2560810Karzhemanov-m5--> </InlineEquation> is its (wild) automorphism and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8350_Article_IEq6.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="94" /> </InlineMediaObject> <EquationSource Format="TEX">\(f:X\longrightarrow C\)</EquationSource> <!--LobJMat2560810Karzhemanov-m6--> </InlineEquation> is a <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8350_Article_IEq5.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma\)</EquationSource> <!--LobJMat2560810Karzhemanov-m7--> </InlineEquation>-compatible morphism onto a curve. This settles the most involved case in a conjecture of Z. Reichstein, D. Rogalski, and J.J. Zhang.</p>

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One Instance of Wild Automorphisms

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • I. V. Karzhemanov

摘要

Abstract

We study a class of smooth projective \(3\) -folds admitting wild automorphisms and relate this subject with smooth complete families of Fano varieties. Using isotriviality of some of the latter families we show that certain triples \((X,f,\sigma)\) do not exist, where \(X\) is a smooth projective \(3\) -fold, \(\sigma\) is its (wild) automorphism and \(f:X\longrightarrow C\) is a \(\sigma\) -compatible morphism onto a curve. This settles the most involved case in a conjecture of Z. Reichstein, D. Rogalski, and J.J. Zhang.