论文标题
一类电流的回调操作
A pullback operation on a class of currents
论文作者
论文摘要
对于复杂的歧管$ x $和复杂的Hermitian歧管$ y $之间的任何holomorphic映射$ f \ colon x \ y $，我们将回调$ f^*$从光滑表单扩展到一类电流。我们为这种回调提供了一个基本的演算，并在相当温和的假设下表明它在同一个学上是合理的。我们认为的电流类别尤其包含任何分析周期的Lelong电流。我们的回调一般取决于$ y $的Hermitian结构，但是如果$ f $是淹没，则与通常的电流回调相吻合。该结构基于代数几何形状中的吉林映射。
For any holomorphic mapping $f\colon X\to Y$ between a complex manifold $X$ and a complex Hermitian manifold $Y$ we extend the pullback $f^*$ from smooth forms to a class of currents. We provide a basic calculus for this pullback and show under quite mild assumptions that it is cohomologically sound. The class of currents we consider contains in particular the Lelong current of any analytic cycle. Our pullback depends in general on the Hermitian structure of $Y$ but coincides with the usual pullback of currents in case $f$ is a submersion. The construction is based on the Gysin mapping in algebraic geometry.
