We examine Li’s double determinantal varieties in the special case that they are toric. We recover from the general double determinantal varieties case, via a more elementary argument, that they are irreducible and show that toric double determinantal varieties are smooth. We use this framework to give a straightforward formula for their dimension. Finally, we use the smallest nontrivial toric double determinantal variety to provide some empirical evidence concerning an open problem in local algebra.
Bibliographical noteFunding Information:
The first author was partially supported by the University of Kentucky?s Summer Research & Creativity Fellowship, and the third and fourth authors were partially supported by the Dr. J.C. Eaves Scholarship during the writing of this paper. We are thankful to Courtney George, Chris Manon, Uwe Nagel for helpful conversations. We are also grateful to Seth Sullivant for pointing out to us the connections to algebraic statistics and to the triple Segre product. We thank the referee for a careful reading of and valuable comments on an earlier draft of this manuscript.
© 2021 Taylor & Francis Group, LLC.
- Determinantal varieties
- quiver varieties