The closure of a linear space in a product of lines
| Autor: | Federico Ardila, Adam Boocher |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Betti number
13P10 05E40 05E45 Closure (topology) 0102 computer and information sciences Commutative Algebra (math.AC) 01 natural sciences Matroid Combinatorics Mathematics - Algebraic Geometry FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Ideal (ring theory) 0101 mathematics Algebraic Geometry (math.AG) Mathematics Discrete mathematics Mathematics::Combinatorics Algebra and Number Theory Mathematics::Commutative Algebra Degree (graph theory) Linear space 010102 general mathematics Mathematics - Commutative Algebra 16. Peace & justice 010201 computation theory & mathematics Product (mathematics) Affine space Combinatorics (math.CO) |
| Zdroj: | Journal of Algebraic Combinatorics. 43:199-235 |
| ISSN: | 1572-9192 0925-9899 |
| DOI: | 10.1007/s10801-015-0634-x |
| Popis: | Given a linear space L in affine space A^n, we study its closure L' in the product of projective lines (P^1)^n. We show that the degree, multigraded Betti numbers, defining equations, and universal Grobner basis of its defining ideal I(L') are all combinatorially determined by the matroid M of L. We also prove I(L') and all of its initial ideals are Cohen-Macaulay with the same Betti numbers. In so doing, we prove that the initial ideals of I(L') are the Stanley-Reisner ideals of an interesting family of simplicial complexes related to the basis activities of M. We also describe the state polytope of I(L'), which is related to the matroid basis polytope of M. Comment: 33 pages, 5 figures |
| Databáze: | OpenAIRE |
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