Splittings of Toric Ideals
| Autor: | Graham Keiper, Adam Van Tuyl, Giuseppe Favacchio, Johannes Hofscheier |
|---|---|
| Přispěvatelé: | Favacchio G., Hofscheier J., Keiper G., Van Tuyl A. |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Binomial (polynomial)
Betti number Prime ideal Existential quantification Commutative Algebra (math.AC) 01 natural sciences Combinatorics Integer matrix Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics Graded Betti numbers Graphs Toric ideals Mathematics - Combinatorics 0101 mathematics Mathematics::Symplectic Geometry Mathematics Algebra and Number Theory Simple graph Ideal (set theory) Mathematics::Commutative Algebra Graded Betti numbers Graphs Toric ideals 010102 general mathematics Mathematics::Rings and Algebras 16. Peace & justice Mathematics - Commutative Algebra Settore MAT/02 - Algebra 13D02 13P10 14M25 05E40 Settore MAT/03 - Geometria 010307 mathematical physics Combinatorics (math.CO) |
| ISSN: | 0021-8693 |
| Popis: | Let $I \subseteq R = \mathbb{K}[x_1,\ldots,x_n]$ be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal $I$ can be "split" into the sum of two smaller toric ideals. For a general toric ideal $I$, we give a sufficient condition for this splitting in terms of the integer matrix that defines $I$. When $I = I_G$ is the toric ideal of a finite simple graph $G$, we give additional splittings of $I_G$ related to subgraphs of $G$. When there exists a splitting $I = I_1+I_2$ of the toric ideal, we show that in some cases we can describe the (multi-)graded Betti numbers of $I$ in terms of the (multi-)graded Betti numbers of $I_1$ and $I_2$. 20 pages, 9 figures; v2: error corrected, improved exposition; v3: revision based on comments from the referee |
| Databáze: | OpenAIRE |
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