Botero, Ana Maria (2022) The Convex-Set Algebra and Intersection Theory on the Toric Riemann-Zariski Space. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 38 (3). pp. 465-486. ISSN 1439-8516, 1439-7617
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | BODIES; Convex geometry; intersection theory; toric varieties; b-Chow groups; Riemann-Zariski spaces |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 27 Nov 2023 13:36 |
| Last Modified: | 27 Nov 2023 13:36 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56828 |
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