Toroidal b-divisors and Monge-Amp\`ere measures
Abstract
We generalize the intersection theory of nef toric (Weil) b-divisors on smooth and complete toric varieties to the case of smooth and complete toroidal embeddings. As a key ingredient we show the existence of a limit measure, supported on the weakly embedded 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 toroidal 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.
Keywords
Cite
@article{arxiv.2004.14045,
title = {Toroidal b-divisors and Monge-Amp\`ere measures},
author = {Ana María Botero and José Ignacio Burgos Gil},
journal= {arXiv preprint arXiv:2004.14045},
year = {2021}
}
Comments
Corrected version taking into account suggestions of the referee. The proof of the Hilbert--Samuel formula has been modified