  We study the intersections of general Schubert varieties X_w with permuted
big cells, and give an inductive degeneration of each such "Schubert patch" to
a Stanley-Reisner scheme. Similar results had been known for Schubert patches
in various types of Grassmannians. We maintain reducedness using the results of
[Knutson 2007] on automatically reduced degenerations, or through more standard
cohomology-vanishing arguments.
  The underlying simplicial complex of the Stanley-Reisner scheme is a subword
complex, as introduced for slightly different purposes in [Knutson-Miller
2004], and is homeomorphic to a ball. This gives a new proof of the
Andersen-Jantzen-Soergel/Billey and Graham/Willems formulae for restrictions of
equivariant Schubert classes to fixed points.
