  We discuss black hole spacetimes with a geometrically defined quasi-local
horizon on which the curvature tensor is algebraically special relative to the
alignment classification. Based on many examples and analytical results, we
conjecture that a spacetime horizon is always more algebraically special (in
all of the orders of specialization) than other regions of spacetime. Using
recent results in invariant theory, such geometric black hole horizons can be
identified by the alignment type $\textbf{II}$ or $\textbf{D}$ discriminant
conditions in terms of scalar curvature invariants, which are not dependent on
spacetime foliations. The above conjecture is, in fact, a suite of conjectures
(isolated vs dynamical horizon; four vs higher dimensions; zeroth order
invariants vs higher order differential invariants). However, we are
particularly interested in applications in four dimensions and especially the
location of a black hole in numerical computations.
