Local cohomology of bivariate splines (Q1358928)

The use of homological algebra in spline theory was introduced by \textit{L. Billera} [Trans. Am. Math. Soc. 310, 325-340 (1988; Zbl 0718.41017)]. The authors consider in this paper the problem of determining the dimension of the space of bivariate splines on a given connected finite simplicial complex. This problem is closely related to the freeness of a certain \(R\)-module, where \(R = {\mathbb{R}}[x,y,z]\). Some examples are given.