Roever Lecture: "Algebraic Geometry over C for Beginners"

Mark Green, UCLA

Abstract: Classical algebraic geometry is the study of geometric objects defined by polynomial equations.  How do we figure out the geometry from what we know about the equations?  In this talk, I’ll discuss the strategy of allowing the object to become very singular but also very simple, and then using that to reconstruct the original object.  Particularly interesting is the relationship between the homology or cohomology of the singular object and of the original object.  Along the way, the Hodge decomposition will be introduced, and also a beginner’s look at two important classes of singularities—normal crossing singularities and KSBA singularities.  One goal is to understand the relationship between how the variety becomes singular and how the Hodge decomposition becomes singular.  This talk is intended for non-experts.

Host: Matt Kerr

Tea will be served @ 3:45 in room 200