Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Singularities of generic projection hypersurfaces

Seminar | January 21 | 5-6 p.m. | 939 Evans Hall

 Takumi Murayama, Princeton University

 Department of Mathematics

Classically, it is known that every algebraic variety over an algebraically closed field is birational to a hypersurface in some projective space. Using generic linear projections, one can show that this hypersurface can be taken to have at worst nodal singularities in dimension one, or at worst ordinary singularities in dimension two. We present generalizations of these results to arbitrary dimension. In particular, in dimensions up to five, we show that the resulting singularities are those that appear on degenerations of smooth varieties in moduli theory. This result is due to Doherty over the complex numbers, and is joint with Rankeya Datta in positive characteristic.

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