  The quark-meson model is investigated for the two- and three-flavor case
extended by contributions of vector mesons under conditions encountered in
core-collapse supernova matter. Typical temperature ranges, densities and
electron fractions, as found in core-collapse supernova simulations, are
studied by implementing charge neutrality and local beta-equilibrium with
respect to weak interactions. Within this framework, we analyze the resulting
phase diagram and equation of state (EoS) and investigate the impact of
undetermined parameters of the model. The EoS turns out to be relatively
independent on the entropy per baryon but there are significant changes when
going from the two-flavor to the three-flavor case due to the nontrivial
contribution from the strange quarks which stay massive even at high densities.
While an increasing vector meson coupling constant leads to a substantial
stiffening of the EoS, we find that the impact of changing the scalar meson
mass is equally strong and results in a softening of the EoS for increasing
values.
