6533b859fe1ef96bd12b7791
RESEARCH PRODUCT
Regularity and h-polynomials of toric ideals of graphs
Adam Van TuylGiuseppe FavacchioGraham Keipersubject
Hilbert seriesBetti numberGeneral MathematicsDimension (graph theory)0102 computer and information sciencesCommutative Algebra (math.AC)01 natural sciencesRegularityCombinatoricssymbols.namesakeMathematics - Algebraic GeometryCorollaryMathematics::Algebraic GeometryGraded Betti numbers; Graphs; Hilbert series; Regularity; Toric idealsFOS: MathematicsIdeal (ring theory)13D02 13P10 13D40 14M25 05E400101 mathematicsAlgebraic Geometry (math.AG)QuotientHilbert–Poincaré seriesMathematicsSimple graphDegree (graph theory)Mathematics::Commutative AlgebraApplied Mathematics010102 general mathematicsMathematics - Commutative AlgebraSettore MAT/02 - AlgebraToric ideals010201 computation theory & mathematicsGraded Betti numbers Graphs Hilbert series Regularity Toric idealssymbolsSettore MAT/03 - GeometriaGraded Betti numbersGraphsdescription
For all integers 4 ≤ r ≤ d 4 \leq r \leq d , we show that there exists a finite simple graph G = G r , d G= G_{r,d} with toric ideal I G ⊂ R I_G \subset R such that R / I G R/I_G has (Castelnuovo–Mumford) regularity r r and h h -polynomial of degree d d . To achieve this goal, we identify a family of graphs such that the graded Betti numbers of the associated toric ideal agree with its initial ideal, and, furthermore, that this initial ideal has linear quotients. As a corollary, we can recover a result of Hibi, Higashitani, Kimura, and O’Keefe that compares the depth and dimension of toric ideals of graphs.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-03-16 |