Time: 9h30, Thursday, September 19, 2019
Location: Rom 611 - 612, Building A6, Institute of Mathematics

Abstract: A Newton polyhedron is a positive integral convex polyhedron closed under the translations along the axis. Such a polyhedron corresponds to a monomial ideal. The maximum dimension of the non-compact facets of the Newton polyhedron is a well-known algebraic invariant of the ideal. There is a conjecture saying that this invariant is not less than that of the unmixed part of the ideal. We will show that the Newton polyhedron of the unmixed part of a monomial ideal is the intersection of the positive linear half-spaces supporting the non-compact proper facets of the original Newton polyhedron. This description will be used to settle the conjecture.