Advisor: Vladimir Baranovsky
Abstract:
We begin by exploring algebraic codes created using cubic hypersurfaces. This leads to the questions of classification, realization, and construction of cubic hypersurfaces. Given the classification by Manin, Frame, Swinnerton-Dyer, etc., we will look at methods of realization and construction of these cubics. Specifically, we will focus on two approaches. The first approach involves looking at the blow-downs of cubics. The second approach involves automorphisms of well-defined cubics.