Geodesic
Note on the Grothendieck Group of Subspaces of Rational Functions and Shokurov's Cartier b-divisors
Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 562-572

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DOI

In a previous paper the authors developed an intersection theory for subspaces of rational functions on an algebraic variety $X$ over $\mathbf{k}\,=\,\mathbb{C}$ . In this short note, we first extend this intersection theory 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 group of the semigroup of subspaces of rational functions on $X$ . The constructed isomorphism moreover preserves the intersection numbers. This provides an alternative point of view on Cartier $b$ -divisors and their intersection theory.
DOI : 10.4153/CMB-2013-039-6
Mots-clés : 14C20, 14Exx, intersection number, Cartier divisor, Cartier b-divisor, Grothendieck group 
Kaveh, Kiumars; Khovanskii, A. G. Note on the Grothendieck Group of Subspaces of Rational Functions and Shokurov's Cartier b-divisors. Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 562-572. doi: 10.4153/CMB-2013-039-6
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     title = {Note on the {Grothendieck} {Group} of {Subspaces} of {Rational} {Functions} and {Shokurov's} {Cartier} b-divisors},
     journal = {Canadian mathematical bulletin},
     pages = {562--572},
     year = {2014},
     volume = {57},
     number = {3},
     doi = {10.4153/CMB-2013-039-6},
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