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- W4298266603 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 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." @default.
- W4298266603 created "2022-10-01" @default.
- W4298266603 creator A5029079985 @default.
- W4298266603 date "2017-01-14" @default.
- W4298266603 modified "2023-10-18" @default.
- W4298266603 title "Intersection theory of toric $b$-divisors in toric varieties" @default.
- W4298266603 doi "https://doi.org/10.48550/arxiv.1701.03925" @default.
- W4298266603 hasPublicationYear "2017" @default.
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