 
Summary: The chain property for the associated
primes of Agraded 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 Agraded 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 Agraded 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 Agraded 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 Agraded if it is
Z d homogeneous via A and, moreover, if it has the Hilbert function
dim C
C [x] Æ
I
