Botero, Ana Maria and Gil, Jose Ignacio Burgos (2022) Toroidal b-divisors and Monge-Ampere measures. MATHEMATISCHE ZEITSCHRIFT, 300 (1). pp. 579-637. ISSN 0025-5874, 1432-1823
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We generalize the intersection theory of nef toric (Weil) b-divisors on smooth and complete toric varieties to the case of nef b-divisors on complete varieties which are toroidal with respect to a snc divisor. As a key ingredient we show the existence of a limit measure, supported on a balanced rational conical polyhedral space attached to the toroidal embedding, which arises as a limit of discrete measures defined via tropical intersection theory on the polyhedral space. We prove that the intersection theory of nef Cartier b-divisors can be extended continuously to nef toroidal Weil b-divisors and that their degree can be computed as an integral with respect to this limit measure. As an application, we show that a Hilbert-Samuel type formula holds for big and nef toroidal Weil b-divisors.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | BODIES; FANS; b-divisors; Convex analysis; Polyhedral spaces; Tropical geometry; Monge-Ampere measures |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Klaus Künnemann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 Aug 2022 09:36 |
| Last Modified: | 17 Aug 2022 09:36 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46531 |
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