Local cohomology of bivariate splines

[摘要] We consider the problem of determining the dimension of the space of bivariate splines C-k(r)(Delta), for all k. This problem is closely related to the question of whether C-r(<(Delta)over cap>) is a free R-module. The main result is that C-r(<(Delta)over cap>) is free if and only if \Delta\ has genus zero and C-k(r)(Delta) has the expected dimension for k=r+1 (and hence for all k). We also obtain several interesting corollaries, including the following simple non-freeness criterion: given a fixed Delta having an edge with both vertices interior, and which does not extend to the boundary, there exists an r(0), which can be determined by inspection, such that C-r(<(Delta)over cap>) is not free for any r greater than or equal to r(0). (C) 1997 Elsevier Science B.V.

[发布日期] 1997-05-01

[效力级别]  Proceedings Paper