Local cohomology of bivariate splines
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Publication:1358928
DOI10.1016/S0022-4049(97)00026-1zbMath0902.41010OpenAlexW1975715261MaRDI QIDQ1358928
Michael Stillman, Henry K. Schenck
Publication date: 6 December 1998
Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0022-4049(97)00026-1
Projective and free modules and ideals in commutative rings (13C10) Spline approximation (41A15) Local cohomology and commutative rings (13D45)
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Cites Work
- Unnamed Item
- The dimension of bivariate spline spaces of smoothness r for degree \(d\geq 4r+1\)
- Modules of piecewise polynomials and their freeness
- Modules of splines on polyhedral complexes
- On the dimension of bivariate spline spaces of smoothness r and degree \(d=3r+1\)
- Homology of Smooth Splines: Generic Triangulations and a Conjecture of Strang