Thermodynamics with 2+1 and 3 flavors of improved staggered quarks

We present preliminary results from exploring the phase diagram of finite temperature QCD with three degenerate flavors and with two light flavors and the mass of the third held approximately at the strange quark mass. We use an order _x000B_2s a2, a4 Symanzik improved gauge action and an order _x000B_sa2, a4 improved staggered quark action. The improved staggered action leads to a dispersion relation with diminished lattice artifacts, and hence better thermodynamic properties. It decreases the flavor symmetry breaking of staggered quarks substantially, and we estimate that at the transition temperature for an Nt = 8 to Nt = 10 lattice all pions will be lighter than the lightest kaon. Preliminary results on lattices with Nt = 4, 6 and 8 are presented.