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<p>In this paper, we establish several integrated defect relations in the sense of Nevanlinna, as well as non-integrated defect relations in the spirit of Fujimoto-Cai-Ru, for meromorphic maps from complete K<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40627_2025_162_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ddot{a}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>a</mi> <mo>¨</mo> </mover> </math></EquationSource> </InlineEquation>hler manifolds —whose universal coverings are biholomorphic to balls in <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40627_2025_162_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {C}^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>—into projective varieties intersecting divisors. Our approach uses the recently introduced concept of Green-Griffiths <i>p</i>-germs by Etesse. These results extend our earlier work on defect relations for holomorphic maps from complete Riemann surfaces into projective varieties.</p>

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Defect relations for meromorphic maps of complete K\({\ddot{a}}\)hler manifolds into projective varieties

  • 期刊论文

  • 发表日期：

    2025年8月28日

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  • Qili Cai,
  • Min Ru,
  • Chin Jui Yang

摘要

In this paper, we establish several integrated defect relations in the sense of Nevanlinna, as well as non-integrated defect relations in the spirit of Fujimoto-Cai-Ru, for meromorphic maps from complete K \(\ddot{a}\) a ¨ hler manifolds —whose universal coverings are biholomorphic to balls in \(\mathbb {C}^p\) C p —into projective varieties intersecting divisors. Our approach uses the recently introduced concept of Green-Griffiths p-germs by Etesse. These results extend our earlier work on defect relations for holomorphic maps from complete Riemann surfaces into projective varieties.