8 problems

Let $P$ be a $G$-invariant polytope, and suppose that $H^*(P;G)[t]$ is an effective polynomial. Stapledon's positive-coefficient conjecture. If the coefficient of $t^m$ in the ordi…

Let $P$ be a $G$-invariant lattice polytope. For each $g\in G$, define the evaluation $H^*(P;G)1$ of the equivariant volume at $g$. Stapledon's equivariant volume conjecture. For e…

Let $P$ be a $G$-invariant lattice polytope, and let $Y$ be the corresponding toric variety with torus-invariant line bundle $L$. The equivariant $H^*$-series is the series…

Let $G$ be a finite group, let $M$ be a lattice, let $\rho:G\to\operatorname{Aff}(M)$ be an affine representation, and let $P$ be a $G$-invariant lattice polytope. Assume that…

Let $G$ be a finite group, let $M$ be a lattice of rank $d$, and let $\rho:G\to\operatorname{Aff}(M)$ be an affine representation. Let $P\subset M_\mathbb{R}$ be a $G$-invariant…

Let $G$ be a finite group acting on a lattice, and let $P$ be a $G$-invariant lattice polytope. Let $Y$ be the toric variety with ample line bundle $L$ associated to $P$, and let…

Let $G$ be a finite group acting on a lattice polytope $P$, and let $H^*[z]=\sum_{j\geq 0}H^*_jz^j$ be its equivariant $H^*$-series. Let $h^*[z]$ be the ordinary $h^*$-polynomial o…

Let $G$ be a finite group acting on a lattice polytope $P\subseteq\mathbb{R}^n$. Let $M$ be the sublattice obtained by translating the affine span of $P$ to the origin, and let…