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 cone 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.

中文翻译：

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关于 Bott-Samelson 变体的 Mori 理论和 Newton-Okounkov 体

我们证明在 Bott-Samelson 变体X 上，每个可移动除数都是 nef。这使我们能够考虑有效因数的 Zariski 分解，进而产生有效锥的 Mori 室分解的描述。这相当于来自X 的所有可能的双有理态射的信息。应用这个结果，我们证明了 Bott-Samelson 变体的全局 Newton-Okounkov 锥体相对于所谓的“水平”标志的合理多面体。事实上，我们证明了相应全局值半群的有限生成的更强性质。