Oct. 15, 2007

David Eisenbud

Plato's Cave: Mapping a variety to a hypersurface

Algebraic curves in space were first studied by projecting them linearly to plane curves; and surfaces were studied similarly, projecting them to hypersurfaces in 3-space. General projections in these dimensions are very nice, but there are strange new phenomena in high dimensions. What can be said in general? What could one hope for? I'll describe the classical theory, and then some current questions from my recent work on the high-dimensional case.

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