Skip to Main content Skip to Navigation
Journal articles

Bounds on the dimension of trivariate spline spaces: A homological approach

Abstract : We consider the vector space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain partitioned into tetrahedra. We prove new lower and upper bounds on the dimension of this space by applying homological techniques. We give an insight of different ways of approaching this problem by exploring its connections with the Hilbert series of ideals generated by powers of linear forms, fat points, the so-called Fröberg--Iarrobino conjecture, and the weak Lefschetz property.
Document type :
Journal articles
Complete list of metadata

Cited literature [26 references]  Display  Hide  Download

https://hal.inria.fr/hal-00879100
Contributor : Bernard Mourrain Connect in order to contact the contributor
Submitted on : Wednesday, February 26, 2014 - 6:13:12 PM
Last modification on : Saturday, January 27, 2018 - 1:32:10 AM
Long-term archiving on: : Monday, May 26, 2014 - 12:55:35 PM

File

Mourrain-Villamizar.pdf
Files produced by the author(s)

Identifiers

Collections

`

Citation

Bernard Mourrain, Nelly Villamizar. Bounds on the dimension of trivariate spline spaces: A homological approach. Mathematics in Computer Science, Springer, 2014, 8 (2), pp.157-174. ⟨10.1007/s11786-014-0187-8⟩. ⟨hal-00879100v2⟩

Share

Metrics

Record views

460

Files downloads

359