Abstract:We prove that every smooth complete toric variety can be made projective by a finite sequence of toric blow-ups along smooth torus-invariant centers. More precisely, for any smooth complete fan $\Sigma$ in $\mathbb{R}^n$, after fixing an ordered lattice basis, there is a canonical smooth complete projective fan $\widehat{\Sigma}$ refining $\Sigma$, and the induced toric morphism $X_{\widehat{\Sigma}} \to X_\Sigma$ factors as a finite composition of blow-ups along smooth torus-invariant subvarieties of codimension at least two. The construction combines three ingredients: a projective wall-arrangement fan canonically attached to $\Sigma$, a sign-adaptation algorithm that refines $\Sigma$ to a smooth fan subordinate to the wall-arrangement fan using only codimension-two blow-ups, and a barycentric derived subdivision that forces projectivity. The proof is uniform in all dimensions.
| Comments: | 10 pages, 3 figures |
| Subjects: | Algebraic Geometry (math.AG) |
| MSC classes: | 14M25, 52B20, 14E05 |
| Cite as: | arXiv:2605.25013 [math.AG] |
| (or arXiv:2605.25013v1 [math.AG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25013 arXiv-issued DOI via DataCite (pending registration) |
From: Parsa Bakhtary [view email]
[v1]
Sun, 24 May 2026 11:35:27 UTC (14 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。