Seminar
| Parent Program: | |
|---|---|
| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
How to (sometimes) glue and split toric ideals, and the consequences
Gluing two semigroups is an operation originally used to classify monomial curves that are complete intersections. It produces a new semigroup whose associated toric ideal is the sum of the two original toric ideals, plus a gluing binomial. This cannot always be done. The splitting operation is a kind of reverse operation where a toric ideal splits as the sum of two toric ideals. For both operations one would like to construct the syzygies of the big toric ideal from the syzygies of the two smaller parts. During this talk, we will see how homogeneous semigroups can always be glued by embedding them suitably in a higher dimensional space. That will produce a toric ideal that splits. In particular, we will see that two toric ideals associated to graphs always occur as the splitting of a toric ideal associated to a graph or a 3-regular hypergraph whose minimal graded free resolution is the tensor product of the resolutions of the
two smaller original ideals. This talk is based on past and ongoing work with Hema Srinivasan.