• Corpus ID: 244709774

Complexity of the usual torus action on Kazhdan-Lusztig varieties

@inproceedings{DontenBury2021ComplexityOT,
  title={Complexity of the usual torus action on Kazhdan-Lusztig varieties},
  author={Maria Donten-Bury and Laura Escobar and Irem Portakal},
  year={2021}
}
We investigate the class of Kazhdan-Lusztig varieties, and its subclass of matrix Schubert varieties, endowed with a naturally defined torus action. Writing a matrix Schubert variety Xw as Xw = Yw × C (where d is maximal possible), we show that Yw can be of complexity-k exactly when k 6= 1. Also, we give a combinatorial description of the extremal rays of the weight cone of a Kazhdan-Lusztig variety, which in particular turns out to be the edge cone of an acyclic directed graph. Finally, we use… 

Figures from this paper

References

SHOWING 1-10 OF 48 REFERENCES
Flags, Schubert polynomials, degeneracy loci, and determinantal formulas
Under appropriate conditions on the rank function r, which guarantee that, for generic h, f,(h) is irreducible, we prove a formula for the class [f,(h)] of this locus in the Chow or cohomology ring
Patch ideals and Peterson varieties
AbstractPatch ideals encode neighbourhoods of a variety in GLn/B. For Peterson varieties we determine generators for these ideals and show they are complete intersections, and thus Cohen–Macaulay and
Polyhedral Divisors and Algebraic Torus Actions
We provide a complete description of normal affine varieties with effective algebraic torus action in terms of what we call proper polyhedral divisors on semiprojective varieties. Our approach
A Gröbner basis for Kazhdan-Lusztig ideals
{\it Kazhdan-Lusztig ideals}, a family of generalized determinantal ideals investigated in [Woo-Yong~'08], provide an explicit choice of coordinates and equations encoding a neighborhood of a
Gröbner geometry of Schubert polynomials
Given a permutation w ?? Sn, we consider a determinantal ideal Iw whose generators are certain minors in the generic n ?~ n matrix (filled with independent variables). Using ?emultidegrees?f as
The Geometry of T-Varieties
This is a survey of the language of polyhedral divisors describing T-varieties. This language is explained in parallel to the well established theory of toric varieties. In addition to basic
Bumpless pipe dreams encode Gr\"obner geometry of Schubert polynomials
In their study of infinite flag varieties, Lam, Lee, and Shimozono (2021) introduced bumpless pipe dreams in a new combinatorial formula for double Schubert polynomials. These polynomials are the T
An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson
This paper provides an introduction to equivariant cohomology and homology using the approach of Goresky, Kottwitz, and MacPherson. When a group G acts suitably on a variety X, the equivariant
...
1
2
3
4
5
...