Cohen-Macaulay fiber cones

Details Cohen-Macaulay fiber cones Cohen-Macaulay fiber cones

2002-12-09

arxiv.org/abs/math/0212119v1

Mathematics

Commutative Algebra

16 pages, appeared in "Commutative Algebra, Algebraic Geometry and Computational Methods", proceedings of the 1996 Hanoi confe

Scientific paper

Cohen Macaulay property of fiber cones of ideals is characterized in terms of its Hilbert series. Hilbert series of fiber cones of ideals with minimal mixed multiplicity is calculated. It is proved that the fiber cone of an m-primary ideal I with minimal mixed multiplicity is Cohen-Macaulay if and only if its reduction number is atmost one. Hilbert series of fiber cones of ideals generated by quadratic sequences in standard graded rings is computed by deforming it to a face ring of a simplicial complex. Applications are given to defining ideals of monomial projective space curves lying on the quadric xw-yz=0, straightening-closed ideals in graded algebras with straightening law and Huckaba-Huneke ideals of analytic spread 1 and 2.

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