关于有理函数子空间的Grothendieck群和Shokurov b-因子的注记
Note on the Grothendieck group of subspaces of rational functions and Shokurov's b-divisors
摘要：
在以前的论文中，作者发展了复数上代数簇X上的有理函数的子空间的相交理论。本文首先将这种相交理论推广到任意代数闭基域。其次给出了X的双有理类上的b-因子群与X上的有理函数的子空间半群的Grothendieck群之间的同构。所构造的同构还保持了相交数。这为b因子及其相交理论提供了一种替代方法。
英文摘要：
In a previous paper the authors develop an intersection theory for subspaces of rational functions on an algebraic variety X over complex numbers. In this note, we first extend this intersection theory to an arbitrary algebraically closed ground field. Secondly we give an isomorphism between the group of b-divisors on the birational class of X and the Grothendieck group of the semigroup of subspaces of rational functions on X. The constructed isomorphism moreover preserves the intersection numbers. This provides an alternative approach to b-divisors and their intersection theory.
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