Patch ideals and Peterson varieties

By Erik Insko, Alexander Yong. 2011

48 citations recorded by the source corpus.

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 Gorenstein. Consequently, we — combinatorially describe the singular locus of the Peterson variety;— give an explicit equivariant K-theory localization formula; and— extend some results of [B. Kostant ‘96] and of D. Peterson to intersections of Peterson varieties with Schubert varieties. We conjecture that the tangent cones are Cohen–Macaulay, and that their h-polynomials are nonnegative and upper-semicontinuous. Similarly, we use patch ideals to briey analyze other examples of torus invariant subvarieties of GLn/B, including Richardson varieties and Springer fibers.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0d872bbe40f90db0ac3c09b2043e983befcc8cc3

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In Discrete Mathematics and Combinatorics

1. M. Masuda
2. T. Horiguchi
3. Hiraku Abe
4. Megumi Harada
5. T. Panov
6. D. Suh
7. Suyoung Choi
8. V. Buchstaber

In Geometry and Topology

1. M. Masuda
2. T. Horiguchi
3. Hiraku Abe
4. Megumi Harada
5. T. Panov
6. D. Suh
7. Suyoung Choi

In Mathematical Physics

1. Hiraku Abe
2. Megumi Harada
3. M. Masuda
4. T. Horiguchi

Citations in the corpus

• The cohomology rings of regular nilpotent Hessenberg varieties in Lie type A (2015, background): “Both of the above types of Hessenberg varieties have been much studied, and it is known, for example, that Hess(N, h) is irreducible [4] and possibly singular [31, 28], while Hess(S, h) is smooth, and possibly non-connected [11].”