Joint Algebra and Geometry/Geometry and Topology Seminar

Cohomology of the space of polynomial morphisms on A^1 with prescribed ramifications

Oishee Banerjee, Department of Mathematics, University of Chicago,

In this talk we will discuss the moduli spaces Simp^m_ⁿ of degree n + 1 morphisms A¹_^K with "ramification length <m" over an algebraically closed field K. For each m, the moduli space Simp^m_ⁿ is a Zariski open subset of the space of degree n + 1 polynomials over K up to ^Aut⁽A¹_^K). It is, in a way, orthogonal to the many papers about polynomials with prescribed zeroes - here we are prescribing, instead, the ramification data. We will also see why and how our results align, in spirit, with the long standing open problem of understanding the topology of the Hurwitz space.

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For more information, please contact Math Dept. by phone at 626-395-4335 or by email at [email protected].