  We present multi-frequency radio observations of the 2010 nova event in the
symbiotic binary V407 Cygni, obtained with the Karl G. Jansky Very Large Array
and spanning 1-45 GHz and 17-770 days following discovery. This nova---the
first ever detected in gamma rays---shows a radio light curve dominated by the
wind of the Mira giant companion, rather than the nova ejecta themselves. The
radio luminosity grew as the wind became increasingly ionized by the nova
outburst, and faded as the wind was violently heated from within by the nova
shock. This study marks the first time that this physical mechanism has been
shown to dominate the radio light curve of an astrophysical transient. We do
not observe a thermal signature from the nova ejecta or synchrotron emission
from the shock, due to the fact that these components were hidden behind the
absorbing screen of the Mira wind.
  We estimate a mass loss rate for the Mira wind of Mdot_w ~ 10^-6 M_sun/yr. We
also present the only radio detection of V407 Cyg before the 2010 nova, gleaned
from unpublished 1993 archival VLA data, which shows that the radio luminosity
of the Mira wind varies by a factor of >~20 even in quiescence. Although V407
Cyg likely hosts a massive accreting white dwarf, making it a candidate
progenitor system for a Type Ia supernova, the dense and radially continuous
circumbinary material surrounding V407 Cyg is inconsistent with observational
constraints on the environments of most Type Ia supernovae.
