On the Mori theory and Newton-Okounkov bodies of Bott-Samelson varieties

Georg Merz; David Schmitz; Henrik Seppänen

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arXiv · 1709.09910

On the Mori theory and Newton-Okounkov bodies of Bott-Samelson varieties

Georg Merz·David Schmitz·Henrik Seppänen

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Abstract

We prove that on a Bott-Samelson variety $X$ every movable divisor is nef. This enables us to consider Zariski decompositions of effective divisors, which in turn yields a description of the Mori chamber decomposition of the effective cone. This amounts to information on all possible birational morphisms from $X$. Applying this result, we prove the rational polyhedrality of the global Newton-Okounkov body of a Bott-Samelson variety with respect to the so called `horizontal' flag. In fact, we prove the stronger property of the finite generation of the corresponding global value semigroup.

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Georg Merz, David Schmitz, Henrik Seppänen. 2017-09-28. On the Mori theory and Newton-Okounkov bodies of Bott-Samelson varieties. https://arxiv.org/abs/1709.09910

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