  Patch ideals encode neighbourhoods of a variety in GL_n/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 projectivized tangent cones are
Cohen-Macaulay, and that their h-polynomials are nonnegative and
upper-semicontinuous. Similarly, we use patch ideals to briefly analyze other
examples of torus invariant subvarieties of GL_n/B, including Richardson
varieties and Springer fibers.
