双理性的一个特征性的自由准则
A characteristic free criterion of birationality
摘要：
一个发展{ \em ab initio}理论的理性/双理性映射约，但不一定是不可约的，投影品种在任意特征。引入了有理映射的一个数值不变量，称为雅可比对偶秩。证明了在这种一般情况下，有理映射是双有理的当且仅当其雅可比对偶秩达到其最大可能值。即使在源簇不可约的“经典”情况下，这个不变量在映射的度上也有一些增益，因为它一方面与交换代数中的自然构造内在相关，另一方面，它是有效地直接可计算的。应用程序给出的结果，到目前为止只知道在特征零。特别是，令人惊讶的结果Dolgachev有关的程度，平面极地克雷莫纳地图给出了一个替代的概念角度。
英文摘要：
One develops {\em ab initio} the theory of rational/birational maps over reduced, but not necessarily irreducible, projective varieties in arbitrary characteristic. A numerical invariant of a rational map is introduced, called the Jacobian dual rank. It is proved that a rational map in this general setup is birational if and only if the Jacobian dual rank attains its maximal possible value. Even in the "classical" case where the source variety is irreducible there is some gain for this invariant over the degree of the map as it is, on one hand, intrinsically related to natural constructions in commutative algebra and, on the other hand, is effectively straightforwardly computable. Applications are given to results so far only known in characteristic zero. In particular, the surprising result of Dolgachev concerning the degree of a plane polar Cremona map is given an alternative conceptual angle.
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