Oops, all Hilbert! Hilbert functions, h-polynomials, and the Hilbertian property
- Event Type
- Lecture
- Sponsor
- Algebra, Geometry, Combinatorics Seminar
- Location
- 3217 Everitt
- Date
- Sep 7, 2023 3:00 pm
- Speaker
- Ada Stelzer (UIUC)
- Contact
- Alexander Yong
- ayong@illinois.edu
- Views
- 49
Many fundamental properties of projective varieties are encoded by their Hilbert functions, which record dimensions of the graded pieces of their coordinate rings. A variety is called Hilbertian if its Hilbert function is a polynomial. We will introduce these notions from the ground up before explaining the ubiquity of Hilbertian varieties in combinatorial commutative algebra via Stanley-Reisner theory. If time permits we will also discuss possible generalizations of these ideas to multigraded settings.