Generalized splines and graphic arrangements

详细信息    查看全文

• 作者：Michael DiPasquale
• 关键词：Generalized splines ; Hyperhomology ; Graphic arrangements ; Multi ; arrangements ; Logarithmic derivations ; Multi ; derivations ; Chordal graphs
• 刊名：Journal of Algebraic Combinatorics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：45
• 期：1
• 页码：171-189
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Combinatorics; Convex and Discrete Geometry; Order, Lattices, Ordered Algebraic Structures; Computer Science, general; Group Theory and Generalizations;
• 出版者：Springer US
• ISSN：1572-9192
• 卷排序：45

文摘

We define a chain complex for generalized splines on graphs, analogous to that introduced by Billera and refined by Schenck–Stillman for splines on polyhedral complexes. The hyperhomology of this chain complex yields bounds on the projective dimension of the ring of generalized splines. We apply this construction to the module of derivations of a graphic multi-arrangement, yielding homological criteria for bounding its projective dimension and determining freeness. As an application, we show that a graphic arrangement admits a free constant multiplicity if and only if it splits as a product of braid arrangements.