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- W2564485334 abstract "We examine the integral cohomology rings of certain families of $2n$-dimensional orbifolds $X$ that are equipped with a well-behaved action of the $n$-dimensional real torus. These orbifolds arise from two distinct but closely related combinatorial sources, namely from characteristic pairs $(Q,lambda)$, where $Q$ is a simple convex $n$-polytope and $lambda$ a labelling of its facets, and from $n$-dimensional fans $Sigma$. In the literature, they are referred as toric orbifolds and singular toric varieties respectively. Our first main result provides combinatorial conditions on $(Q,lambda)$ or on $Sigma$ which ensure that the integral cohomology groups $H^{ast}(X)$ of the associated orbifolds are concentrated in even degrees. Our second main result assumes these condition to be true, and expresses the graded ring $H^*(X)$ as a quotient of an algebra of polynomials that satisfy an integrality condition arising from the underlying combinatorial data. Also, we compute several examples." @default.
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- W2564485334 date "2017-10-04" @default.
- W2564485334 modified "2023-10-14" @default.
- W2564485334 title "On the integral cohomology ring of toric orbifolds and singular toric varieties" @default.
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- W2564485334 doi "https://doi.org/10.2140/agt.2017.17.3779" @default.
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