Algebraic Geometry Seminar: A Decomposition of Hurwitz Space
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In this talk we will describe a natural decomposition of the Hurwitz space $\mathcal{H}_{d,g}$ parametrizing simply-branched covers of $\mathbb{P}^1$. By studying the geometry of this decomposition, we will deduce the irreducibility of the Gieseker-Petri locus $\mathcal{GP}^1_{d} \subset \mathcal{M}_{g}$ where $d = \frac{g+2}{2}$. Furthermore, we will explain the role this decomposition plays in establishing upper bounds for slopes of sweeping curves in the $d$-gonal locus.
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