Year: 2018
Type: preprint
Abstract: In this article, we study properties of the exponential Hilbert series of a $G$-equivariant projective variety, where $G$ is a semisimple, simply-connected complex linear algebraic group. We prove a relationship between the exponential Hilbert series and the degree and dimension of the variety. We then prove a combinatorial identity for the coefficients of the polynomial representing the exponential Hilbert series. This formula is used in examples to prove further combinatorial identities involving Stirling numbers of the first and second kinds.
Source: arXiv (Cornell University)
Author: Johnson, Wayne A.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2797855967