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The topology of the zero locus of a genus 2 theta function


Author: Kevin Kordek
Journal: Trans. Amer. Math. Soc. 370 (2018), 5131-5153
MSC (2010): Primary 14H15, 14H42, 20F38
DOI: https://doi.org/10.1090/tran/7127
Published electronically: February 26, 2018
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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.


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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
Email: kevin.kordek@math,gatech.edu

DOI: https://doi.org/10.1090/tran/7127
Received by editor(s): October 3, 2015
Received by editor(s) in revised form: November 13, 2016
Published electronically: February 26, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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