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Dissertation
Quasi-Spline Sheaves and their Contact Ideals
Doctor of Philosophy (Ph.D.), Drexel University
May 2016
DOI:
https://doi.org/10.17918/etd-7317
Abstract
We research quasi-spline sheaves, which are an algebraic geometric generalization of spline spaces. Spline spaces are vector spaces of splines that are defined over some polyhedral complex in real space, and the dimension and basis for them are of interest. Billera found that certain spline spaces are determined by ideals that are affine forms that vanish on the intersections of the maximal faces of the complex. These ideals correspond to contact ideals of a quasi-spline sheaf, and we ask if quasi-spline sheaves are determined by contact ideals in the same way. A quasi-spline sheaf or spline space can be defined by identifying ideals, called ideal difference-conditions. We find that the contact ideals are a canonical example of ideal difference-conditions for a quasi-spline sheaf. Next, we ask how to find the contact ideals of a quasi-spline sheaf when only ideal differenceconditions are given. Last, we find a complex for any quasi-spline sheaf and try to figure out when this gives a resolution for the quasi-spline sheaf. If it is a resolution, it gives an alternative way to compute the dimension of a quasi-spline sheaf, or any spline space.
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Details
- Title
- Quasi-Spline Sheaves and their Contact Ideals
- Creators
- Timothy Hayes - DU
- Contributors
- Patrick Clarke (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- iv, 81 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 7317; 991014632593404721