Scholarlink

Abstract <p> We show that every smooth cubic hypersurface <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8534_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(X\)</EquationSource> </InlineEquation> in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8534_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb P^{n+1}\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8534_Article_IEq3.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\ge 2\)</EquationSource> </InlineEquation>, is algebraically elliptic in Gromov’s sense. This gives the first examples of nonrational projective manifolds elliptic in Gromov’s sense. We also deduce that the punctured affine cone over <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11501_2025_8534_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(X\)</EquationSource> </InlineEquation> is elliptic. </p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Algebraic Gromov’s Ellipticity of Cubic Hypersurfaces

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年6月1日

查看全文
  • Shulim Kaliman,
  • Mikhail Zaidenberg

摘要

Abstract

We show that every smooth cubic hypersurface \(X\) in \(\mathbb P^{n+1}\) , \(n\ge 2\) , is algebraically elliptic in Gromov’s sense. This gives the first examples of nonrational projective manifolds elliptic in Gromov’s sense. We also deduce that the punctured affine cone over \(X\) is elliptic.