摘要翻译：
这是[Ca01]=Math.AG/0110051的续集。我们定义了几何轨道的双亚纯{\IT范畴}。这些插值在（紧K\\“ahler）流形和这类具有对数结构的流形之间。这些几何轨道是从其几何的观点来考虑的，因此配备了变体的通常不变量：态射和双亚纯映射、微分形式、基本群和泛覆盖、定义域和有理点。这里建立了最基本的性质，直接从没有轨道结构的变种的情况中改编而来。[Ca01]的论点可以直接适用于将主结构结果推广到这个轨道范畴。我们希望稍后再回到更深的方面。其动机是，紧致k“ahler（和复射影）流形分类理论的自然框架至少包括轨道范畴，如[Ca01]所示，它通过将{it特殊}流形分解为轨道塔，或者是$\kappa_+=-\infty$或$\kappa=0$,而且似乎也通过最小模型程序，其中大多数证明只在附加”边界“之后才起作用。此外，纤维在几何轨道的双亚纯范畴中享有在没有轨道结构的变种范畴中不满足的扩展性质，允许表示总空间的不变量与一般纤维的不变量和基底的不变量。例如，基本群的自然序列在那里是精确的；此外，总空间是特殊的，如果是通用纤维和基地。这使得该类别适合将具有$\kappa_+=-\infty$或$\kappa=0$的orbifolds属性提升到特殊属性。
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英文标题：
《Orbifoldes speciales et classification bimeromorphe des varietes
  kaehleriennes compactes》
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作者：
Frederic Campana
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最新提交年份：
2009
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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：
  This is a sequel to [Ca01]=math.AG/0110051. We define the bimeromorphic {\it category} of geometric orbifolds. These interpolate between (compact K\" ahler) manifolds and such manifolds with logarithmic structure. These geometric orbifolds are considered from the point of view of their geometry, and thus equipped with the usual invariants of varieties: morphisms and bimeromorphic maps, differential forms, fundamental groups and universal covers, fields of definition and rational points. The most elementary properties, directly adapted from the case of varieties without orbifold structure, are established here. The arguments of [Ca01] can then be directly adapted to extend the main structure results to this orbifold category. We hope to come back to deeper aspects later. The motivation is that the natural frame for the theory of classification of compact K\" ahler (and complex projective) manifolds includes at least the category of orbifolds, as shown in [Ca01] by the fonctorial decomposition of {\it special} manifolds as tower of orbifolds with either $\kappa_+=-\infty$ or $\kappa=0$, and also, seemingly, by the minimal model program, in which most proofs work only after the adjunction of a "boundary".   Also, fibrations enjoy in the bimeromorphic category of geometric orbifolds extension properties not satisfied in the category of varieties without orbifold structure, permitting to express invariants of the total space from those of the generic fibre and of the base. For example, the natural sequence of fundamental groups is exact there; also the total space is special if so are the generic fibre and the base. This makes this category suitable to lift properties from orbifolds having either $\kappa_+=-\infty$ or $\kappa=0$ to those which are special.
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PDF链接：
https://arxiv.org/pdf/0705.0737