Search results for "Hilbert–Poincaré series"

showing 3 items of 3 documents

Universal formulas for characteristic classes on the Hilbert schemes of points on surfaces

2007

This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on the affine plane by proving a result on the existence of certain universal formulas expressing characteristic classes on the Hilbert schemes in term of Nakajima's creation operators. The purpose of this work is (at least) two-fold. First of all, we clarify the notion of ``universality'' of certain formulas about the cohomology of the Hilbert schemes by defining a universal algebra of creation operators. This helps us to reformulate and extend a lot of the f…

Hilbert manifoldHilbert's basis theoremHilbert matrix01 natural sciencesMathematics - Algebraic Geometrysymbols.namesakeCharacteristic classesPrimary 14C05Secondary 14C170103 physical sciencesFOS: Mathematics[MATH]Mathematics [math]0101 mathematicsAlgebraic Geometry (math.AG)ComputingMilieux_MISCELLANEOUSMathematicsHilbert–Poincaré seriesHilbert's second problemHilbert series and Hilbert polynomialAlgebra and Number Theory010102 general mathematicsHilbert's fourteenth problemUniversal formulasPrimary 14C05; Secondary 14C17Hilbert schemes of pointsAlgebraHilbert schemesymbols[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physics
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Regularity and h-polynomials of toric ideals of graphs

2020

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.

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 numbersGraphs
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MULTIPLICITIES IN THE MIXED TRACE COCHARACTER SEQUENCE OF TWO 3 × 3 MATRICES

2006

We find explicitly the multiplicities in the (mixed) trace cocharacter sequence of two 3 × 3 matrices over a field of characteristic 0 and show that asymptotically they behave as polynomials of seventh degree. As a consequence we obtain also the multiplicities of certain irreducible characters in the cocharacter sequence of the polynomial identities of 3 × 3 matrices.

Symmetric functionsymbols.namesakePure mathematicsPolynomialSequenceTrace (linear algebra)Degree (graph theory)General MathematicssymbolsField (mathematics)Invariant theoryMathematicsHilbert–Poincaré seriesInternational Journal of Algebra and Computation
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