DMS Linear Algebra/Algebra Seminar

Speaker: Douglas A. Leonard

Title: What information should a desingularization tree have?

Abstract: Standard weak desingularization (or resolution of singularities) techniques are based on blowups, with a directed tree having arcs labelled by blowups, nodes labelled by (polynomial, variety) and the Jacobian criterion to generate new arcs.

My methods (to get a strong desingularization) are based on unimodular transformations, as labels on arcs, (poly, ineq, eq, valuation) on nodes, and Initial monomials and weights as criteria for partitioning to generate new arcs.

I'll run a few examples of my new Macaulay2 code versus Singular's resolve.lib code to show how these differ.