When is the matroid Schubert variety Q-Gorenstein?

Start with a linear subspace of complex n-space. Then, take its closure in the product of n projective lines. The closure is an algebraic variety that has been given the name "matroid Schubert variety." It is maybe most famous for playing a central role in June Huh and Botong Wang's proof of the Dowling-Wilson conjecture.

In this talk, I will define what it means for a normal variety to be Gorenstein and Q-Gorenstein, respectively. (These two properties can be thought of as measuring how far a variety is from being smooth.) The matroid Schubert variety is often not smooth, so it is interesting to consider under which circumstances the matroid Schubert variety is Gorenstein and Q-Gorenstein, respectively. I will present a result that answers this question using only the combinatorial information of the original linear subspace. To conclude, I will compute a concrete example.