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arXiv · 1509.08221

The infinite topology of the hyperelliptic locus in Torelli space

Kevin Kordek
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Abstract

Genus $g$ Torelli space is the moduli space of genus $g$ curves of compact type equipped with a homology framing. The hyperelliptic locus is a closed analytic subvariety consisting of finitely many mutually isomorphic components. We use properties of the hyperelliptic Torelli group to show that when $g\geq 3$ these components do not have the homotopy type of a finite CW complex. Specifically, we show that the second rational homology of each component is infinite-dimensional. We give a more detailed description of the topological features of these components when $g=3$ using properties of genus 3 theta functions.

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Kevin Kordek. 2015-09-28. The infinite topology of the hyperelliptic locus in Torelli space. https://arxiv.org/abs/1509.08221

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