  Henize 2-10 is a dwarf starburst galaxy hosting a $\sim10^{6}~M_{\odot}$
black hole (BH) that is driving an ionized outflow and triggering star
formation within the central $\sim100$ pc of the galaxy. Here we present ALMA
continuum observations from 99 to 340 GHz, as well as spectral line
observations of the molecules CO (1-0, 3-2), HCN (1-0, 3-2), and HCO$^{+}$
(1-0, 3-2), with a focus on the BH and its vicinity. Incorporating cm-wave
radio measurements from the literature, we show that the spectral energy
distribution of the BH is dominated by synchrotron emission from 1.4 to~340 GHz
with a spectral index of $\alpha\approx-0.5$. We analyze the spectral line data
and identify an elongated molecular gas structure around the BH with a velocity
distinct from the surrounding regions. The physical extent of this molecular
gas structure is $\approx130~{\rm pc}\times30$ pc and the molecular gas mass is
$\sim10^{6}~M_{\odot}$. Despite an abundance of molecular gas in this general
region, the position of the BH is significantly offset from the peak intensity,
which may explain why the BH is radiating at a very low Eddington ratio. Our
analysis of the spatially-resolved line ratio between CO J=3-2 and J=1-0
implies that the CO gas in the vicinity of the BH is highly excited,
particularly at the interface between the BH outflow and the regions of
triggered star formation. This suggests that the cold molecular gas is being
shocked by the bipolar outflow from the BH, supporting the case for positive BH
feedback.
