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<p>In this paper, we give a result on finiteness of meromorphic mappings from <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_64_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb C^m\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="double-struck">C</mi> <mi>m</mi> </msup> </math></EquationSource> </InlineEquation> into <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_64_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb P^n(\mathbb C)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi mathvariant="double-struck">P</mi> <mi>n</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> sharing hyperplanes in general position with truncated multiplicities to level <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_64_Article_IEq5.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>n</mi> </math></EquationSource> </InlineEquation>. In our result, the number of shared hyperplanes is just <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_64_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(2n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation> instead of <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_64_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(2n+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_64_Article_IEq8.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(2n+2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> as in the previous results, but the number of involving meromorphic mappings still does not exceed 2.</p>

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Finiteness of meromorphic mappings sharing \(2n\) hyperplanes in \(\mathbb P^n(\mathbb C)\) with truncated multiplicities

  • 期刊论文

  • 发表日期：

    2025年2月21日

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  • H. T. Thuy,
  • P. D. Thoan,
  • N. T. Nhung

摘要

In this paper, we give a result on finiteness of meromorphic mappings from \(\mathbb C^m\) C m into \(\mathbb P^n(\mathbb C)\) P n ( C ) sharing hyperplanes in general position with truncated multiplicities to level \(n\) n . In our result, the number of shared hyperplanes is just \(2n\) 2 n instead of \(2n+1\) 2 n + 1 or \(2n+2\) 2 n + 2 as in the previous results, but the number of involving meromorphic mappings still does not exceed 2.