  We report R~4300 VLT SINFONI adaptive optics integral field K-band
spectroscopy of the nucleus of the Seyfert 1 galaxy NGC3227 at a spatial
resolution of 0.085" (7pc). We present the morphologies and kinematics of
emission lines and absorption features, and give the first derivation of a
black hole mass in a Seyfert 1 nucleus from spatially resolved stellar
dynamics. We show that the gas in the nucleus has a mean column density of
order 10^{24}-10^{25}cm^{-2} and that it is geometrically thick, in agreement
with the standard `molecular torus' scenario. We discuss which heating
processes may be responsible for maintaining the vertical height of the torus.
We have also resolved the nuclear stellar distribution, and find that within a
few parsecs of the AGN there has been an intense starburst, the most recent
episode of which began ~40Myr ago but has now ceased. The current luminosity of
stars within 30pc of the AGN, ~3x10^9L_sun, is comparable to that of the AGN.
Based on a comparison of the respective size scales, we argue that the star
formation has been occuring in the obscuring torus. Finally, we present the
first derivation of a black hole mass in a Seyfert 1 nucleus from stellar
dynamics which marginally spatially resolve the black hole's sphere of
influence. We apply Schwarzschild orbit superposition models to our full
2-dimensional data and derive the mass of the black hole, paying careful
attention to the input parameters which are often uncertain: the contribution
of the large scale bulge and its mass-to-light ratio; the recent star formation
in the nucleus and its mass-to-light ratio; the contribution of the gas mass to
the potential; and the inclination. Our models yield a 1sigma range for the
black hole mass of M_{BH} = 7x10^6-2x10^7M_sun.
