Lattice polytopes with a given $h^*$-polynomial
| dc.creator | Batyrev, Victor | |
| dc.date | 2006-02-26 | |
| dc.date | 2006-03-16 | |
| dc.date.accessioned | 2026-07-07T07:03:48Z | |
| dc.date.available | 2026-07-07T07:03:48Z | |
| dc.description | Let $Δ\subset \R^n$ be an $n$-dimensional lattice polytope. It is well-known that $h_Δ^*(t) := (1-t)^{n+1} \sum_{k \geq 0} |kΔ\cap \Z^n| t^k $ is a polynomial of degree $d \leq n$ with nonnegative integral coefficients. Let $AGL(n, \Z)$ be the group of invertible affine integral transformations which naturally acts on $\R^n$. For a given polynomial $h^* \in \Z[t]$, we denote by $C_{h^*}(n)$ the number $AGL(n, \Z)$-equivalence classes of $n$-dimensional lattice polytopes such that $h^* = h_Δ^*(t)$. In this paper we show that $\{C_{h^*}(n) \}_{n \geq 1}$ is a monotone increasing sequence which eventually becomes constant. This statement follows from a more general combinatorial result whose proof uses methods of commutative algebra. | |
| dc.description | 10 pages. AMS-LaTeX, some typos were corrected | |
| dc.identifier | https://arxiv.org/abs/math/0602593 | |
| dc.identifier | http://arxiv.org/abs/math/0602593 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109114 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 52B20; 13H10; 14M25 | |
| dc.title | Lattice polytopes with a given $h^*$-polynomial | |
| dc.type | text |