Canadian mathematical bulletin | |
Note on the Grothendieck Group of Subspaces of Rational Functions and Shokurov's Cartier b-divisors | |
A. G. Khovanskii1  Kiumars Kaveh2  | |
[1] Department of Mathematics, University of Toronto, Toronto, ON;Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA | |
关键词: intersection number; Cartier divisor; Cartier b-divisor; Grothendieck group; | |
DOI : 10.4153/CMB-2013-039-6 | |
学科分类:数学(综合) | |
来源: University of Toronto Press * Journals Division | |
【 摘 要 】
In a previous paper the authors developed an intersection theory forsubspaces of rational functions on an algebraic variety $X$ over $mathbf{k} = mathbb{C}$. In this short note, we first extend this intersectiontheory to an arbitrary algebraically closed ground field $mathbf{k}$. Secondly we give an isomorphism between the group of Cartier$b$-divisors on the birational class of $X$ and the Grothendieck groupof the semigroup of subspaces of rational functions on $X$. Theconstructed isomorphism moreover preserves the intersection numbers. This provides an alternative pointof view on Cartier $b$-divisors and their intersection theory.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912050577055ZK.pdf | 13KB | download |