Conic decomposition of a toric variety and its application to cohomology

@inproceedings{Park2021ConicDO,
  title={Conic decomposition of a toric variety and its application to cohomology},
  author={Seonjeong Park and Jongbaek Song},
  year={2021}
}
We introduce the notion of a conic sequence of a convex polytope. It is a way of building up a polytope starting from a vertex and attaching faces one by one with certain regulations. We apply this to a toric variety to obtain an iterated cofibration structure on it. This allows us to prove several vanishing results in the rational cohomology of a toric variety and to calculate Poincaré polynomials for a large class of singular toric varieties. 

Figures from this paper

Torus orbit closures in the flag variety

. The study of torus orbit closures in the (complete) flag variety was initiated by Klyachko and Gelfand–Serganova in the mid-1980s, but it seems that not much has been done since then. In this

My title

Semi-classical processes such as production and decay of electroweak sphaleron in the Standard Model and also microscopic black hole in low scale gravity scenario typically involve large number of

References

SHOWING 1-10 OF 20 REFERENCES

Infinite families of equivariantly formal toric orbifolds

Abstract 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

TORIC VARIETIES

We study toric varieties over a field k that split in a Galois extension K/k using Galois cohomology with coefficients in the toric automorphism group. This Galois cohomology fits into an exact

On Integral Cohomology of Certain Orbifolds

The CW-complex structure of certain spaces, such as effective orbifolds, can be too complicated for computational purposes. In this paper we develop the concept of $\mathbf{q}$-CW complex structure

Homology and cohomology of toric varieties

  • Arno Jordan
  • Mathematics
    Konstanzer Schriften in Mathematik und Informatik / Universität Konstanz / Fakultät für Mathematik und Informatik
  • 1998
The theory of toric varieties plays an important role as a bridge between algebraic geometry, combinatorial convex geometry, and commutative algebra. The interpretation and application of many

Poincaré polynomials of generic torus orbit closures in Schubert varieties

The closure of a generic torus orbit in the flag variety G / B G/B of type  A A is known to be a permutohedral variety, and its Poincaré polynomial agrees with the

The numbers of faces of simplicial polytopes

In this paper is considered the problem of determining the possiblef-vectors of simplicial polytopes. A conjecture is made about the form of the sclution to this problem; it is proved in the case

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

Stringy Geometry and Topology of Orbifolds

This is a survey article on the recent development of "stringy geometry and topology of orbifolds", a new subject of mathematics motivated by orbifold string theory.