A defect relation for holomorphic curves intersecting hypersurfaces
A defect relation for holomorphic curves intersecting hypersurfaces
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DOI：
10.1353/ajm.2004.0006
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发表时间：
2004-01
影响因子：
1.7
通讯作者：
M. Ru
中科院分区：
文献类型：
--
作者：
M. Ru
1933年，H. Cartan在[inline-graphic xmlns：xlink =“http：//www.w3.org/1999/xlink”xlink：href=“02 i”/]中证明了线性非退化全纯曲线f：[inline-graphic xmlns：xlink =” http://www.w3.org/1999/xlink“xlink：href=“01 i”/]和超平面Hj，1 ≤ j ≤ q的亏格关系<$qj =1 δ f（Hj）≤ n + 1.本文将其推广到与超曲面相交的全纯曲线。1979年，B。Shiffman证明了，如果f：[inline-graphic xmlns：xlink=”http://www.w3.org/1999/xlink“xlink：href=“03 i”/]是代数非退化全纯映射，且D1，. . .，Dq是[inline-graphic xmlns：xlink=”http://www.w3.org/1999/xlink“xlink：href=“04 i”/]中一般位置的超曲面，则Dq j =1 δ f（Dj）≤ n + 1.本文证明了这一猜想。
In 1933, H. Cartan proved a defect relation Σ q j =1 δ f ( H j ) ≤ n + 1 for a linearly nondegenerate holomorphic curve f : [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] and hyperplanes H j , 1 ≤ j ≤ q , in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] in general position. This paper extends it to holomorphic curves intersecting hypersurfaces. In 1979, B. Shiffman conjectured that if f : [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /] is an algebraically non-degenerate holomorphic map, and D 1 , . . . , D q are hypersurfaces in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="04i" /] in general position, then Σ q j =1 δ f ( D j ) ≤ n + 1. This paper proves this conjecture.