论文标题
与庞加莱等级1的2捆2捆绑包与庞贝拉杆1
Rank 2 Bundles with Meromorphic Connections with Poles of Poincaré Rank 1
论文作者
论文摘要
$ \ mathbb c \ times m $，$ m $一个复杂的歧管上的全态矢量捆绑包，具有poles poles ofPoincaré等级1沿$ \ {0 \} \ times m $的meromorphic Connections自然出现在代数的几何形状中。它们在这里称为$（te）$ - 结构。本文采用抽象的观点。它给出了所有$（TE）$的完整分类 - 等级2的结构在细菌上$ \ big（m，t^0 \ big）$的$。对于每点$ m $，它们分为四种类型。三种类型的那些具有通用的展开，第四类（对数类型）不具有通用的展开。 $（te）$ - 第四类结构的分类是丰富而有趣的。本文找到和列表也是所有$（te）$ - 基本意义上的结构：它们共同引起所有排名$ 2 $ $（te）$ - 结构，并且每个列表中的任何其他$（te）$ - 结构都不会引起每个排名。他们的基本空间$ m $变成了带有Euler Fields的二维$ f $ manifolds。本文还为每个这样的$ f $ - manifold提供了所有等级2 $（TE）$ - 结构的分类。同样，这种分类非常丰富。纸的骨干是正常形式。尽管诱导的希格斯田和基地空间的几何形状和几何形状也很重要并且被考虑。
Holomorphic vector bundles on $\mathbb C\times M$, $M$ a complex manifold, with meromorphic connections with poles of Poincaré rank 1 along $\{0\}\times M$ arise naturally in algebraic geometry. They are called $(TE)$-structures here. This paper takes an abstract point of view. It gives a complete classification of all $(TE)$-structures of rank 2 over germs $\big(M,t^0\big)$ of manifolds. In the case of $M$ a point, they separate into four types. Those of three types have universal unfoldings, those of the fourth type (the logarithmic type) not. The classification of unfoldings of $(TE)$-structures of the fourth type is rich and interesting. The paper finds and lists also all $(TE)$-structures which are basic in the following sense: Together they induce all rank $2$ $(TE)$-structures, and each of them is not induced by any other $(TE)$-structure in the list. Their base spaces $M$ turn out to be 2-dimensional $F$-manifolds with Euler fields. The paper gives also for each such $F$-manifold a classification of all rank 2 $(TE)$-structures over it. Also this classification is surprisingly rich. The backbone of the paper are normal forms. Though also the monodromy and the geometry of the induced Higgs fields and of the bases spaces are important and are considered.
