Generalized multiplicities of edge ideals

Autor:	Alilooee, Ali, Soprunov, Ivan, Validashti, Javid
Rok vydání:	2016
Předmět:	Mathematics - Commutative Algebra Mathematics - Algebraic Geometry Mathematics - Combinatorics 13H15 13D40 52B20
Zdroj:	Journal of Algebraic Combinatorics, May (2018), Volume 47, Issue 3, pp. 441--472
Druh dokumentu:	Working Paper
Popis:	We explore connections between the generalized multiplicities of square-free monomial ideals and the combinatorial structure of the underlying hypergraphs using methods of commutative algebra and polyhedral geometry. For instance, we show the $j$-multiplicity is multiplicative over the connected components of a hypergraph, and we explicitly relate the $j$-multiplicity of the edge ideal of a properly connected uniform hypergraph to the Hilbert-Samuel multiplicity of its special fiber ring. In addition, we provide general bounds for the generalized multiplicities of the edge ideals and compute these invariants for classes of uniform hypergraphs. Comment: 24 pages, 6 figures. The results of Theorem 4.6 and Theorem 9.2 are now more general. To appear in Journal of Algebraic Combinatorics
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1607.00733 Zobrazit plný text záznamu View this record from Arxiv