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Local cohomology of bivariate splines

✍ Scribed by Hal Schenck; Mike Stillman

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
791 KB
Volume
117-118
Category
Article
ISSN
0022-4049

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✦ Synopsis

We consider the problem of determining the dimension of the space of bjvariate splines CL(d), for all k. This problem is closely related to the question of whether C'(d) is a free R-module. The main result is that C'( 6) is free if and only if (Al has genus zero and CL(d) 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 A having an edge with both vertices interior, and which does not extend to the boundary, there exists an ro, which can be determined by inspection, such that C'(a) is not free for any r 2 ro. @ 1997 Elsevier Science B.V.

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In [G. Nu rnberger and Th. Riessinger, Numer. Math. 71 (1995), 91 119], we developed an algorithm for constructing point sets at which unique Lagrange interpolation by spaces of bivariate splines of arbitrary degree and smoothness on uniform type triangulations is possible. Here, we show that simila