Abstract
We describe conjecturally the generalized Samuel multiplicities of a monomial ideal
in terms of its Newton polyhedron
More precisely, we conjecture that ci equals the sum of the normalized
-volumes of pyramids over the projections of the
-dimensional compact faces of
along the infinite-directions of i-unbounded facets in which they are contained. For c0 proofs are known (Guibert, Jeffries and Montaño) and for
a proof is given.
2010 Mathematics Subject Classification:
Acknowledgments
We are grateful to the referees, whose comments improved the presentation.