Mathematical Sciences: Research in the Deformation Theory ofSubvarieties of Higher Codimension

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This award supports the research in Algebraic Geometry of Dr. Herbert Clemens of the University of Utah. Professor Clemens will work on the geometry of the generic quintic threefold and on general questions arising from the conjecture that this threefold can carry only finitely many rational curves. Techniques that he will use are the pushforward construction from the theory of D- modules and the infinitesimal Abel-Jacobi map, among others. This is research in the field of Algebraic Geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from Algebra, but from Analysis and Topology, and conversely is finding application in those fields as well as in theoretical Computer Science and in Robotics.