Matroidal Polynomials Have Rational Singularities

  • Dan Bath (KU Leuven)
E1 05 (Leibniz-Saal)


We introduce the class of matroidal polynomials. They are (possibly inhomogeneous) polynomials attached to a matroid and axiomatized by Deletion-Contraction identities. When homogeneous they are matroid support polynomials--polynomials whose monomial support are the bases of a matroid. We show that matroidal polynomials have rational singularities, provided the underlying matroid is connected of rank at least two. The proof is jet-theoretic and involves controlling the dimension of certain jet loci.

By similar methods we show flag matroidal polynomials (attached to a flag of matroids) and Feynman integrands (attached to a Feynman diagram) have rational singularities. When the Feynman diagram satisfies general kinematics, this proves: the Feynman integral in Lee-Pomeransky form is the Mellin transformation of a polynomial with rational singularities.

Our goal is to explain most of these concepts as well as the matrimony between matroids and jets.

Joint with Uli Walther.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of this Seminar