Date: Friday, October 27, 2017
Location: 3096 East Hall (3:10 PM to 4:00 PM)
Title: Flatness in algebraic geometry
Abstract: Flatness, originally introduced by Serre for purely algebraic reasons, has found powerful applications to algebraic geometry; in particular, it turns out flatness gives a suitable notion of a family of algebraic varieties, and thus plays an important role in questions of deformations, moduli spaces, and beyond. In this talk, we'll review the algebraic concept of flatness, and use it to define the flatness of a morphism of algebraic varieties. We'll then sketch some basic examples and properties of flat maps, and explore the ways in which algebraic and geometric data behaves in flat families. In particular, we'll attempt to convince the audience that the somewhat unintuitive notion of flatness actually clarifies, rather than obscures, many geometric questions. The focus will be on examples, intuition, and motivation, rather than on formal proof. The talk will be accessible for students currently in 631.
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Speaker: Devlin Mallory
Institution: UM
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