On the volume of a six-dimensional polytope
| dc.creator | Felikson, Anna | |
| dc.creator | Tumarkin, Pavel | |
| dc.date | 2005-02-08 | |
| dc.date.accessioned | 2026-07-07T05:16:48Z | |
| dc.date.available | 2026-07-07T05:16:48Z | |
| dc.description | This note is a comment to the paper by D.R.Heath-Brown and B.Z.Moroz (Math Proc. Camb. Phil. Soc. 125 (1999)). That paper concerns with the projective surface $S$ in $\mathbb{P}^{3}$ defined by the equation $x_{1}x_{2}x_{3}=x_{4}^{3}$. It is shown there that the evaluation of the leading term of the asymptotic formula for the number of rational points of bounded height in $S(\Q)$ is equivalent to the evaluation of the volume of some 6-dimensional polytope $¶$. The volume of $¶$ is known from several papers; we calculate this volume by elementary method using symmetry of the polytope $¶$. We also discuss a combinatorial structure of $¶$. | |
| dc.identifier | https://arxiv.org/abs/math/0502167 | |
| dc.identifier | http://arxiv.org/abs/math/0502167 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74126 | |
| dc.subject | Metric Geometry | |
| dc.title | On the volume of a six-dimensional polytope | |
| dc.type | text |