On a class of toric manifolds arising from simplicial complexes
On a class of toric manifolds arising from simplicial complexes
Given an arbitrary abstract simplicial complex $K$ on $[m]:=\{1,2,\ldots,m\}$, different from the simplex $\Delta_{[m]}$ with $m$ vertices, we introduce and study a canonical $(2m-2)$-dimensional toric manifold $X_K$, associated to the canonical $(m-1)$-dimensional complete regular fan $\Sigma_K$. This construction yields an infinite family of toric manifolds that are not quasitoric and provides a topological proof of the Dehn-Sommerville relations for the associated Bier sphere $\mathrm{Bier}(K)$. Finally, we prove a criterion for orientability of canonical real toric manifolds.
Ivan Limonchenko、Marinko Timotijevi?、Rade ?ivaljevi?
数学
Ivan Limonchenko,Marinko Timotijevi?,Rade ?ivaljevi?.On a class of toric manifolds arising from simplicial complexes[EB/OL].(2025-06-16)[2025-07-23].https://arxiv.org/abs/2506.13547.点此复制
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