Toric double determinantal varieties

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.

Automated summary

We examine Li's double determinantal varieties in the special case that they are toric, showing that they are irreducible and smooth. We provide a straightforward formula for their dimension and offer empirical evidence concerning an open problem in local algebra using the smallest nontrivial toric double determinantal variety.