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arXiv · 2004.14045

Toroidal b-divisors and Monge-Amp\`ere measures

Ana María Botero·José Ignacio Burgos Gil
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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.

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Ana María Botero, José Ignacio Burgos Gil. 2020-04-29. Toroidal b-divisors and Monge-Amp\`ere measures. https://arxiv.org/abs/2004.14045

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