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- W3080811055 abstract "Abstract A complete nonsingular toric variety (called a toric manifold) is over $P$ if its quotient by the compact torus is homeomorphic to $P$ as a manifold with corners. Bott manifolds are toric manifolds over an $n$-cube $I^n$ and blowing them up at a fixed point produces toric manifolds over $operatorname{vc}(I^n)$ an $n$-cube with one vertex cut. They are all projective. On the other hand, Oda’s three-fold, the simplest non-projective toric manifold, is over $operatorname{vc}(I^3)$. In this paper, we classify toric manifolds over $operatorname{vc}(I^n)$$(nge 3)$ as varieties and as smooth manifolds. It consequently turns out that there are many non-projective toric manifolds over $operatorname{vc}(I^n)$ but they are all diffeomorphic, and toric manifolds over $operatorname{vc}(I^n)$ in some class are determined by their cohomology rings as varieties." @default.
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- W3080811055 date "2018-07-05" @default.
- W3080811055 modified "2023-10-16" @default.
- W3080811055 title "Classification of Toric Manifolds over an n-Cube with One Vertex Cut" @default.
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- W3080811055 doi "https://doi.org/10.1093/imrn/rny161" @default.
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