  (Abridged) We present results from dynamical models of core-collapse
supernovae in one spatial dimension, employing a newly-developed Boltzmann
neutrino radiation transport algorithm, coupled to Lagrangean hydrodynamics and
a consistent high-density nuclear equation of state. We focus on shock breakout
and its neutrino signature and follow the dynamical evolution of the cores of
11 M_sun, 15 M_sun, and 20 M_sun progenitors through collapse and the first 250
milliseconds after bounce. We examine the effects on the emergent neutrino
spectra, light curves, and mix of species of artificial opacity changes, the
number of energy groups, the weak magnetism/recoil corrections, nucleon-nucleon
bremsstrahlung, neutrino-electron scattering, and the compressibility of
nuclear matter. Furthermore, we present the first high-resolution look at the
angular distribution of the neutrino radiation field both in the
semi-transparent regime and at large radii and explore the accuracy with which
our tangent-ray method tracks the free propagation of a pulse of radiation in a
near vacuum. Finally, we fold the emergent neutrino spectra with the
efficiencies and detection processes for a selection of modern underground
neutrino observatories and argue that the prompt electron-neutrino breakout
burst from the next galactic supernova is in principle observable and usefully
diagnostic of fundamental collapse/supernova behavior. Though we are not in
this study focusing on the supernova mechanism per se, our simulations support
the theoretical conclusion (already reached by others) that spherical (1D)
supernovae do not explode when good physics and transport methods are employed.
