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The chain property for the associated primes of A-graded ideals
 

Summary: The chain property for the associated
primes of A-graded ideals
Klaus Altmann 
Abstract
We investigate how the chain property for the associated primes of monomial degenerations
of toric (or lattice) ideals can be generalized to arbitrary A-graded monomial ideals. The
generalization works in dimension d = 2, but it fails for d  3.
Moreover, for a certain class of binomial ideals (including the A-graded ones) we present an
explicit cellular primary decomposition.
1 Introduction
(1.1) Challenged by the question of Arnold for the ideals with the easiest Hilbert function,
Sturmfels has invented in [St1] and x10 of [St2] the notion of A-graded ideals. For a given linear
map A : Z n ! Z d with (ker A) \ Z n
0 = 0 an ideal I  C [x 1 ; : : : ; xn ] is called A-graded if it is
Z d -homogeneous via A and, moreover, if it has the Hilbert function
dim C

C [x] Æ
I


  

Source: Altmann, Klaus - Fachbereich Mathematik und Informatik & Institut für Mathematik, Freie Universität Berlin

 

Collections: Mathematics