Title: Intersection theory of toric $b$-divisors in toric varieties.
Abstract:We introduce toric $b$-divisors on complete smooth toric varieties and a notion of integrability of such divisors. We show that under some positivity assumptions toric $b$-divisors are integrable and ...We introduce toric $b$-divisors on complete smooth toric varieties and a notion of integrability of such divisors. We show that under some positivity assumptions toric $b$-divisors are integrable and that their degree is given as the volume of a convex set. Moreover, we show that the dimension of the space of global sections of a nef toric $b$-divisor is equal to the number of lattice points in this convex set and we give a Hilbert--Samuel type formula for its asymptotic growth. This generalizes classical results for classical toric divisors on toric varieties. Finally, we relate convex bodies associated to $b$-divisors with Newton--Okounkov bodies. The main motivation for studying toric $b$-divisors is that they locally encode the singularities of the invariant metric on an automorphic line bundle over a toroidal compactification of a mixed Shimura variety of non-compact type.Read More
Publication Year: 2017
Publication Date: 2017-01-14
Language: en
Type: preprint
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Cited By Count: 2
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