Commutative Algebra and Algebraic Geometry: A new approach to contact problems in geometry

Seminar | March 14 | 3:45-4:45 p.m. | 939 Evans Hall | Note change in time

 Joe Harris, Harvard University

 Department of Mathematics

Geometric problems involving order of contact—for example, how many flexes does a plane curve of degree $d$ have?---can often be solving by considering the relevant bundle of principle parts. When we're dealing with a family of varieties, though—for example, in a pencil of plane curves of degree $d$, how many have hyperflexes?---difficulties arise: some members of the family will have singularities, and at those singularities the bundle of relative principle parts will no longer be locally free. We will describe two approaches to dealing with this problem: one proposed and carried out by Ziv Ran, and a new one found by Anand Patel and Ashvin Swaminathan.