The PIMS Postdoctoral Fellow Seminar: Emanuela Marangone

For a standard-graded polynomial ring R, the d-Veronese subring is generated as a k-algebra by degree d monomials, is Koszul, and its defining ideal is quadratic, binomial, and determinantal. In this talk, I will discuss what happens if we instead start with a non-standard graded polynomial ring.
 

In joint work with A. Seceleanu, L. Fiorindo, B. Chase, T. de Holleben, S. Singh, T. Nguyen, we determine properties of two-dimensional weighted Veronese rings and, more generally, normal affine semigroup rings, including determinantal presentation, Gröbner basis, graded Hilbert series and graded Betti numbers, and their Koszul property.
 

In contrast, in three or more variables, these properties no longer hold in general. We provide explicit examples where the ring fails to be determinantal and Koszul.