The Convex-Set Algebra and Intersection Theory on the Toric Riemann–Zariski Space

查看全文 作　　者：Ana María [1]BOTERO 机构地区：[1]Institut Für Mathematik,Universität Regensburg,Universitätsstr.31,93053,Regensberg,Germany 出　　处：《Acta Mathematica Sinica,English Series》索引2022年第38卷第3期,共22页 基　　金：Supported by the SFB Higher Invariants at the University of Regensburg。 摘　　要：In previous work of the author,a top intersection product of toric b-divisors on a smooth complete toric variety is defined.It is shown that a nef toric b-divisor corresponds to a convex set and that its top inetersection number equals the volume of this convex set.The goal of this article is to extend this result and define an intersection product of sufficiently positive toric b-classes of arbitrary codimension.For this,we extend the polytope algebra of McMullen to the so called convex-set algebra and we show that it embeds in the toric b-Chow group.In this way,the convex-set algebra can be viewed as a ring for an intersection theory for sufficiently positive toric b-classes.As an application,we show that some Hodge type inequalities are satisfied for the convex set algebra. 关 键 词：Convex geometry intersection theory toric varieties b-Chow groups Riemann–Zariski spaces