复曲面前变和亚环面作用
Toric Prevarieties and Subtorus Actions
摘要：
在环面簇的定义中去掉分离性，人们得到环面前簇的更一般的概念。复曲面前变在代数几何中作为环境空间出现，而且它们自然地作为商构造中的中间步骤出现。我们首先提供了一个完整的描述范畴的复曲面prevariants凸几何数据，所谓的系统的球迷。在第二部分中，我们考虑的行动subtori H的大环面的环面的复曲面前品种X和调查，这样的行动。利用我们的fans系统的语言，我们刻画了H在X上作用的好的前件的存在性。此外，我们通过一个算法构造证明了H在X上的作用总是存在一个复曲面预商，这意味着从X到复曲面预簇Y的一个H-不变复曲面态射p使得每个从X到复曲面预簇的H-不变复曲面态射都通过p因子. Cox，我们证明了每一个复复曲面预簇都是复仿射空间的开复曲面子簇的范畴预商的象。
英文摘要：
Dropping separatedness in the definition of a toric variety, one obtains the more general notion of a toric prevariety. Toric prevarieties occur as ambient spaces in algebraic geometry and moreover they appear naturally as intermediate steps in quotient constructions. We first provide a complete description of the category of toric prevarieties in terms of convex-geometrical data, so-called systems of fans. In a second part, we consider actions of subtori H of the big torus of a toric prevariety X and investigate quotients for such actions. Using our language of systems of fans, we characterize existence of good prequotients for the action of H on X. Moreover, we show by means of an algorithmic construction that there always exists a toric prequotient for the action of H on X, that means an H-invariant toric morphism p from X to a toric prevariety Y such that every H-invariant toric morphism from X to a toric prevariety factors through p. Finally, generalizing a result of D. Cox, we prove that every toric prevariety occurs as the image of a categorical prequotient of an open toric subvariety of some complex affine space.
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