Remark 19.6.25731294EE36CA

Remark 19.6.25.731294EE36CA As a special case of this construction, suppose that $\Gamma $ is the test curve induced by a test configuration as in example 17.14.10 and 17.14.14, then for any $\tau <\Gamma _{\max }$, $\Delta _{Y_{\bullet }}(\theta ,\Gamma _{\tau })$ is the Okounkov body of a graded linear series

where $\mathcal{F}$ is the filtration induced by the test configuration. See [Theorem 5.28, Xia21] for the details. In particular, in this case, our theory of partial Okounkov bodies recovers the Okounkov bodies of the filtered linear series in the sense of [BC11].