URegina Topology & Geometry Seminar: Evan Sundbo

We will see the definition and some examples of broken toric varieties and balloon animal maps between them. After an overview of some of the many different areas in which they appear, we look at how their geometry can be studied via complexes of sheaves on an associated complex of polytopes. This yields results such as a version of the Decomposition Theorem and identifying the weight and Leray filtrations on the cohomology groups of a broken toric variety.