特殊圆褶菌与变种的二倍体分类
Orbifoldes speciales et classification bimeromorphe des varietes kaehleriennes compactes
摘要：
这是[Ca 01]=math.AG/0110051的续篇。我们定义了几何orbifolds的双纯{ \it范畴}。这些插值（紧K\”ahler）流形和这样的流形与对数结构。这些几何orbifolds被认为是从他们的几何观点，从而配备了通常的不变量品种：态射和双纯映射，微分形式，基本群和普遍覆盖，领域的定义和有理点。最基本的性质，直接适用于没有orbifold结构的品种的情况下，在这里建立。[Ca 01]的参数可以直接适用于将主要结构结果扩展到这个轨道范畴。我们希望以后再回到更深的方面。其动机是紧致K\”ahler分类理论的自然框架（和复射影）流形至少包括orbifolds的范畴，如[Ca 01]中所示，通过{ \it special}流形作为具有$κ_+=-\infty$或$κ=0$的orbifolds的塔的函数分解，并且似乎还通过极小模型程序，其中大多数证明工作后，只有一个“边界”的附加。此外，纤维化在几何轨道折叠的双半纯范畴中享有在没有轨道折叠结构的变种范畴中不满足的扩展性质，允许根据一般纤维和基底的不变量来表达全空间的不变量。例如，基本群的自然序列在那里是正合的;如果类属纤维和基是特殊的，那么全空间也是特殊的。这使得该类别适合于将具有$κ_+=-\infty$或$κ=0$的轨道的性质提升到特殊的轨道。
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 $κ_+=-\infty$ or $κ=0$, 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 $κ_+=-\infty$ or $κ=0$ to those which are special.
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