Date: Monday, September 09, 2013
Location: 3096 East Hall (4:00 PM to 5:00 PM)
Title: Plane Rational Maps with Invariant Two Forms
Abstract: Many dynamically interesting rational maps of the projective plane come equipped with invariant meromorphic two forms. In this talk, I present some joint work with JanLi Lin concerning this phenomenon. I will first explain that one can typically make a birational coordinate change to eliminate zeroes of an invariant two form. Then I will consider the problem of arranging algebraic stability for a rational map that preserves a zerofree meromorphic two form. The main result is that if one can arrange stability 'along the poles' of the two form, then one can make it fully algebraically stable. I will illustrate the result by specializing to the case where the invariant two form is given in affine coordinates by $\frac{dx\wedge dy}{xy}$.
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Speaker: Jeff Diller
Institution: University of Notre Dame
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