The topology of the zero locus of a genus 2 theta function
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Abstract:
Mess showed that the genus 2 Torelli group $T_2$ is isomorphic to a free group of countably infinite rank by showing that the genus 2 Torelli space is homotopy equivalent to an infinite wedge of circles. As an application of his computation, we compute the homotopy type of the zero locus of any classical genus 2 theta function in $\mathfrak {h}_2 \times \mathbb {C}^2$, where $\mathfrak {h}_2$ denotes rank 2 Siegel space. Specifically, we show that the zero locus of any such function is homotopy equivalent to an infinite wedge of 2-spheres.References
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Additional Information
- Kevin Kordek
- Affiliation: Department of Mathematics, Mailstop 3368, Texas A&M University, College Station, Texas 77843-3368
- Address at time of publication: School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, Georgia 30332-0160
- MR Author ID: 1202384
- Email: kevin.kordek@math.gatech.edu
- Received by editor(s): October 3, 2015
- Received by editor(s) in revised form: November 13, 2016
- Published electronically: February 26, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 5131-5153
- MSC (2010): Primary 14H15, 14H42, 20F38
- DOI: https://doi.org/10.1090/tran/7127
- MathSciNet review: 3812105