Geometry and Combinatorics Seminar - Christin Bibby (Math)

Speaker: Christin Bibby (Louisiana State University)

Title: A Leray Model for the Orlik-Solomon Algebra

Abstract: We construct a combinatorial generalization of the Leray models for hyperplane arrangement complements.  Given a matroid and some combinatorial blowup data, we give a presentation for a bigraded (commutative) differential graded algebra.  If the matroid is realizable over C, this is the familiar Morgan model for a hyperplane arrangement complement, embedded in a blowup of projective space.  In general, we obtain a CDGA that interpolates between the Chow ring of a matroid and the Orlik-Solomon algebra.  Our construction can also be expressed in terms of sheaves on combinatorial blowups of geometric lattices.  As a key technical device, we construct a monomial basis via a Gr\"obner basis for the ideal of relations.  Combining these ingredients, we show that our algebra is quasi-isomorphic to the classical Orlik-Solomon algebra of the matroid.