Regularization of closed positive currents and Intersection Theory
Regularization of closed positive currents and Intersection Theory
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发表时间：
2007
影响因子：
0.6
通讯作者：
J. Demailly
中科院分区：
文献类型：
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作者：
J. Demailly
-设X为紧复流形，设T为X上二阶（1,1）的闭合正电流。证明了T是具有小负部的光滑闭合实（1,1）电流序列（Tk）的弱极限。Tk的负部分可以用T的Lelong数来限定，一旦tan束TX的曲率的下界已知。此外，Kiselman消灭多次调和函数的Lelong数的方法通过基于Hormander对∂的L估计的替代方法扩展到流形。然后将这些结果应用于推导解析几何中有关除数或相交理论的各种结果。特别地，我们得到了任意紧流形上有效因子与数值有效因子之间的关系，并证明了具有nef切束的Fujiki类C中的每个流形X都是Kahler。如果D是Kahler流形中的有效因子，我们也得到了一个一般的自交不等式，给出了D的常多重层的度的界，用上同调类{D}∈H（X， IR）中的多项式表示。
— LetX be a compact complex manifold and let T be a closed positive current of bidegree (1, 1) on X . It is shown that T is the weak limit of a sequence (Tk) of smooth closed real (1, 1)-currents with small negative part. The negative part of the Tk ’s can be bounded in terms of the Lelong numbers of T , once a lower bound for the curvature of the tangent bundle TX is known. Moreover, Kiselman’s procedure for killing Lelong numbers of a plurisubharmonic function is extended to manifolds by an alternative method based on Hormander’s L estimates for ∂. These results are then applied to derive various results concerning divisors or intersection theory in the context of analytic geometry. Especially, we obtain a relation between effective and numerically effective divisors on arbitrary compact manifolds, and we show that every manifold X in the Fujiki class C with nef tangent bundle is Kahler. If D is an effective divisor in a Kahler manifold, we also obtain a general self-intersection inequality giving a bound of the degrees of the constant multiplicity strata of D, in terms of a polynomial in the cohomology class {D} ∈ H(X, IR).