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摘要翻译：
我们研究了对Kobayashi-Eisenman伪体积形式的对数情形的适应，或者更确切地说，是对Claire Voisin定义的它的变体的适应，她用全纯k-对应来代替全纯映射。对于由复流形X和正交Weil因子组成的对(X，D)，我们定义了一个本征对数伪体积形式\phi_{X，D}。然后我们证明了当X是射影的且K_x+D是充足的时\phi_{X,D}是泛型非退化的。这个结果类似于经典的Kobayashi-Ochiai定理。我们还证明了一类对数k平凡对\phi_{X,D}的消失，这是在对数情形下向关于无穷小测度双曲性的Kobayashi猜想方向迈出的重要一步。
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英文标题：
《Intrinsic pseudo-volume forms for logarithmic pairs》
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作者：
Thomas Dedieu
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Complex Variables 复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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英文摘要：
We study an adaptation to the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, or rather an adaptation of its variant defined by Claire Voisin, for which she replaces holomorphic maps by holomorphic K-correspondences. We define an intrinsic logarithmic pseudo-volume form \Phi_{X,D} for every pair (X,D) consisting of a complex manifold X and a normal crossing Weil divisor, the positive part of which is reduced. We then prove that \Phi_{X,D} is generically non-degenerate when X is projective and K_X+D is ample. This result is analogous to the classical Kobayashi-Ochiai theorem. We also show the vanishing of \Phi_{X,D} for a large class of log-K-trivial pairs, which is an important step in the direction of the Kobayashi conjecture about infinitesimal measure hyperbolicity in the logarithmic case.
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PDF链接：
https://arxiv.org/pdf/0804.4811
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