Geometrically Vertex Decomposable ideals

In combinatorics, vertex decomposition is an inductive method for breaking down simplicial complexes into simpler pieces. Knutson, Miller, and Yong introduced an ideal-theoretic analogue of this procedure, known as geometric vertex decomposition (GVD). This is a special degeneration technique that allows one to recursively decompose an ideal into smaller, simpler pieces while preserving many of their geometric and algebraic properties .

In this talk, I will give an introduction to geometric vertex decomposition and discuss recent results obtained in joint work with E. De Negri, E.Gorla, P. Klein, and J. Rajchgot.