The Hilbert series and $a$-invariant of circle invariants

L. Emily Cowie, Hans-Christian Herbig, Daniel Herden +1

Let $V$ be a finite-dimensional representation of the complex circle ${\mathbb{C}}^{\times }$ determined by a weight vector $\mathbf{a}\in {\mathbb{Z}}^n$. We study the Hilbert series $\op…