The set of toric minimal log discrepancies (Q2459656)

Let \(X\) be a normal toric variety endowed with an effective Weil \({\mathbb{R}}\)-divisor \(B\) which is torus invariant. The pair \((X,B)\) is a toric log variety if \(K_X+B\) is \({\mathbb{R}}\)-Cartier, where \(K_X\) denotes the canonical divisor of \(X\). For any set \(A\subset [0,1]\) containing \(1\) and any integer \(d\geq 1\), let \(M(A,d)\) be the set of minimal log discrepancies \(a(\eta,X,B)\), where \(\eta\in X\) is a Grothendieck point of codimension \(d\) and \((X,B)\) is any toric log variety whose minimal log discrepancies in codimension one lie in \(A\). The author gives an explicit description of the set \(M(A,d)\), and studies its accumulation points. This extends work of \textit{A. Borisov} [Manuscr. Math. 92, No. 1, 33--45 (1997; Zbl 0873.14003)] to the case of toric log varieties; the methods of proof are similar.