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Geometry & Geometric Analysis Seminar

The Geometry and Geometric Analysis (GAGA) Seminar is an opportunity for geometers, topologists, and others from TCU and UT Arlington to learn about new topics of mutual interest. GAGA meets most weeks during the school year. You can find notes from past talks at the GAGA Note Repository, located in a secure off-campus location.

The next meeting of the GAGA Seminar will be on Monday, April 4 at 1:00 in TUC 243. Scott Nollet will be speaking on "Moduli of Distributions."

You can also attend via Zoom.

Abstract: The purpose of this talk is to make a connection between Hilbert schemes and foliations. Jouanolou initiated a study of algebraic foliations on complex projective spaces in 1978, classifying some low degree cases, work that was extended later by various authors. I will be talking about more recent work of Correa, Jardim and collaborators towards classifying more general distributions. They have constructed moduli spaces to classify families of algebraic distributions. Moreover, they have given a morphism from these moduli spaces to Hilbert schemes and described the fibers, thereby giving a way to understand distributions as coming from closed subschemes of projective space, which may behave poorly, i.e. fail to be smooth, irreducible, or reduced.
I’ll start with reminders about how things work in projective algebraic geometry, including the notion of moduli spaces. Then I’ll describe the moduli of distributions, the map to Hilbert schemes. I’ll try to give concrete examples when possible.

Previous Seminars