IANAL abut AFAIK it depends on the school. In general, yeah, the school owns the research. However, it might also possible to get an exclusive or non-exclusive license from your school, again, depending on the school. It will feel funny for a while to pay for your own research but such is life. I must also note that, the school might be willing to grant a non-exclusive license for a relatively small fee (a few grands; no equity) but an exclusive license will most likely set you back a lot more (in cash or in equity).
I co-founded a company based on the research of a classmate years ago and that is exactly what we did. We paid Stanford for a non-exclusive license. I believe Google has done the same for PageRank but for an exclusive license.