  We study the spectral pictures of (jointly) hyponormal 2-variable weighted
shifts with commuting subnormal components. By contrast with all known results
in the theory of subnormal single and 2-variable weighted shifts, we show that
the Taylor essential spectrum can be disconnected. We do this by obtaining a
simple sufficient condition that guarantees disconnectedness, based on the
norms of the horizontal slices of the shift. We also show that for every k >= 1
there exists a k-hyponormal 2-variable weighted shift whose horizontal and
vertical slices have 1- or 2-atomic Berger measures, and whose Taylor essential
spectrum is disconnected.
