# 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…

## References

SHOWING 1-10 OF 48 REFERENCES

Flags, Schubert polynomials, degeneracy loci, and determinantal formulas

- Mathematics
- 1992

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

- Mathematics
- 2011

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

- Mathematics
- 2006

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

- Mathematics
- 2009

{\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

- Mathematics
- 2001

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

- Mathematics
- 2011

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

- Mathematics
- 2021

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

- Mathematics
- 2005

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…