Sasha Gasanova: Invariants of toric double determinantal rings

Abstract.

Double determinantal rings and varieties were introduced by Li as instances of Nakajima quiver varieties, but they are also a natural generalization of classical determinantal rings.

In this talk, we focus on toric double determinantal rings and show that they coincide with the Hibi rings associated to certain finite distributive lattices. Using this fact we compute the number of minimal generators, the multiplicity, the regularity, the a-invariant and the Hilbert function of these toric rings. We also characterize the rings of this class which are Gorenstein, thereby answering a question posed by Li in the toric setting.

This is joint work with J. Biermann, E. De Negri, A. Musapasaoglu, S. Roy.