Oishee Banerjee
Hausdorff Center of Mathematics (Bonn)
November 28, 2019
Cohomology of the space of polynomial morphisms on $\mathbb{A}^1_K$ with prescribed ramifications: In this talk we will discuss the moduli spaces Simp$^m_n$ of degree $n+1$ morphisms $\mathbb{A}^1_{K} \to \mathbb{A}^1_{K}$ 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$(\mathbb{A}^1_{K})$. 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 see why and how our results align, in spirit, with the long standing problem of understanding the topology of the Hurwitz space.
Hausdorff Center of Mathematics (Bonn)
November 28, 2019
Cohomology of the space of polynomial morphisms on $\mathbb{A}^1_K$ with prescribed ramifications: In this talk we will discuss the moduli spaces Simp$^m_n$ of degree $n+1$ morphisms $\mathbb{A}^1_{K} \to \mathbb{A}^1_{K}$ 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$(\mathbb{A}^1_{K})$. 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 see why and how our results align, in spirit, with the long standing problem of understanding the topology of the Hurwitz space.