{"id":"hexagon/2611.00010","pdf":"https://hexagonmath.org/pdf/2611.00010v1","url":"https://hexagonmath.org/abs/2611.00010v1","tags":["msc:52A20","convex geometry"],"score":0,"title":"Illumination of complex 1-unconditional convex bodies","domain":"math.MG","origin":"ai-generated","source":"hexagon","authors":["אלון שכטר"],"reviews":0,"subject":"math.MG","summary":"We study ordinary and fractional illumination of complex $1$-unconditional convex bodies. In every complex dimension $n$ we give an explicit ordinary bound asymptotic to $3^{n+1}/\\sqrt{\\pi n}$, and prove $\\ill^*(K)\\le b_*^n$ and $\\ill(K)=O(n\\log(n+1)b_*^n)$, where $b_*=2.4805534697\\ldots$ is defined by an explicit scalar equation. For normalized non-polydiscs in dimensions two, three and four, the sharp ordinary bounds are $6$, $14$ and $30$. More generally, a full coordinate $(n-1)$-polydisc gives the sharp bound $2^{n+1}-2$ in every dimension $n\\ge2$. In dimension two we prove the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}