arXiv subjects

Jongbaek Song

Publications and source records attributed to Jongbaek Song.

21 records · Page 2Linked to original sources

arXiv2018

Infinite Families of Equivariantly Formal Toric Orbifolds

The simplicial wedge construction on simplicial complexes and simple polytopes has been used by a variety of authors to study toric and related spaces, including non-singular toric varieties, toric manifolds, intersections of quadrics and more generally, polyhedral products. In this paper we extend the analysis to include toric orbifolds. Our main results yield infinite families of toric orbifolds, derived from a given one, whose integral cohomology is free of torsion and is concentrated in even degrees, a property which might be termed \emph{integrally equivariantly formal}. In all cases, it is possible to give a description of the cohomology ring and to relate it to the cohomology of the original orbifold.

math.AT↗

arXiv2017

On integral cohomology of certain orbifolds

The CW structure of certain spaces, such as effective orbifolds, can be too complicated for computational purposes. In this paper we use the concept of $\mathbf{q}$-CW complex structure on an orbifold, to detect torsion in its integral cohomology. The main result can be applied to well known classes of orbifolds or algebraic varieties having orbifold singularities, such as toric orbifolds, simplicial toric varieties, torus orbifolds and weighted Grassmannians.

math.AT↗

arXiv2016

On the Integral Cohomology Ring of Toric Orbifolds and Singular Toric Varieties

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 $(Q,λ)$, where $Q$ is a simple convex $n$-polytope and $λ$ a labelling of its facets, and from $n$-dimensional fans $Σ$. In the literature, they are referred as toric orbifolds and singular toric varieties respectively. Our first main result provides combinatorial conditions on $(Q,λ)$ or on $Σ$ 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.

math.AT↗