Depths of Powers of the Edge Ideal of a Tree

Details Depths of Powers of the Edge Ideal of a Tree Depths of Powers of the Edge Ideal of a Tree

2009-08-04

arxiv.org/abs/0908.0553v1

Mathematics

Commutative Algebra

To appear in Communications in Algebra

Scientific paper

Lower bounds are given for the depths of R/I^t for t at least one when I is
the edge ideal of a tree or forest. The bounds are given in terms of the
diameter of the tree, or in case of a forest, the largest diameter of a
connected component and the number of connected components. These lower bounds
provide a lower bound on the power for which the depths stabilize.

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