Remark 19.3.35AA6A085DBB0

Remark 19.3.3.5AA6A085DBB0 Conversely, maximal-rank valuations of $\mathbb C(X)$ are closely related to flag valuations. More precisely, if a valuation has value group identified with $\mathbb Z^ n_{\mathrm{lex}}$ and maximal rational rank $n$, then [Theorem 2.9, CFKLRS17] shows that it is equivalent¹ to, but not necessarily equal to, a valuation induced by an admissible flag on a modification of $X$.