Barvinok's algorithm and the Todd class of a toric variety (Q1358927)

Let \(X\) denote the toric variety arising from a complete simplicial fan \(\Delta\). In the present article a canonical expression of the Todd class of \(X\) as a power series in the rays of \(\Delta\) is given. An important property of this power series is that its behaviour under (virtual) subdivisions of \(\Delta\) can be described explicitly. Combining this with Barvinok's algorithm [see \textit{A. I. Barvinok}, Math. Oper. Res. 19, No. 4, 769-779 (1994; Zbl 0821.90085)] the author obtains an effective algorithm to compute the Todd class of \(X\). An application of this method to the problem of counting lattice points of a simple lattice polytope is given.