Mathematical Sciences: Normal Singularities

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This project is concerned with various questions about the structure of normal singularities and of maps between varieties. The principal investigator will determine if the product of complete ideals being complete characterizes rational surface singularities. He will study the resolutions of singularities of a normal Cohen-Macauley variety as well as the structure of birational maps between algebraic manifolds. The structure of the local fundamental group of surface singularities in positive characteristic will be investigated. This work lies on the interface of commutative algebra and algebraic geometry. The investigator will examine algebraic structures associated with a surface to see if information can be derived concerning the surface. This is currently a very active area of mathematics.