Is there a smooth lattice polytope which does not have the integer decomposition property?
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917167409135616 |
|---|---|
| author | Hofscheier, Johannes Kasprzyk, Alexander |
| author_facet | Hofscheier, Johannes Kasprzyk, Alexander |
| contents | We introduce Tadao Oda's famous question on lattice polytopes which was originally posed at Oberwolfach in 1997 and, although simple to state, has remained unanswered. The question is motivated by a discussion of the two-dimensional case - including a proof of Pick's Theorem, which elegantly relates the area of a lattice polygon to the number of lattice points it contains in its interior and on its boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20680 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Is there a smooth lattice polytope which does not have the integer decomposition property? Hofscheier, Johannes Kasprzyk, Alexander Combinatorics Algebraic Geometry History and Overview 52B20 (primary), 14M25, 13H10 We introduce Tadao Oda's famous question on lattice polytopes which was originally posed at Oberwolfach in 1997 and, although simple to state, has remained unanswered. The question is motivated by a discussion of the two-dimensional case - including a proof of Pick's Theorem, which elegantly relates the area of a lattice polygon to the number of lattice points it contains in its interior and on its boundary. |
| title | Is there a smooth lattice polytope which does not have the integer decomposition property? |
| topic | Combinatorics Algebraic Geometry History and Overview 52B20 (primary), 14M25, 13H10 |
| url | https://arxiv.org/abs/2512.20680 |