Professor Jens Funke jens.funke@durham.ac.uk
Professor
The geometric theta correspondence for Hilbert modular surfaces
Funke, Jens; Millson, John
Authors
John Millson
Abstract
We give a new proof and an extension of the celebrated theorem of Hirzebruch and Zagier [17] that the generating function for the intersection numbers of the Hirzebruch-Zagier cycles in (certain) Hilbert modular surfaces is a classical modular form of weight 2. In our approach we replace Hirzebuch’s smooth complex analytic compactification of the Hilbert modular surface with the (real) Borel-Serre compactification. The various algebro-geometric quantities that occur in [17] are replaced by topological quantities associated to 4-manifolds with boundary. In particular, the “boundary contribution” in [17] is replaced by sums of linking numbers of circles (the boundaries of the cycles) in 3-manifolds of type Sol (torus bundle over a circle) which comprise the Borel-Serre boundary.
Citation
Funke, J., & Millson, J. (2014). The geometric theta correspondence for Hilbert modular surfaces. Duke Mathematical Journal, 163(1), 65-116. https://doi.org/10.1215/00127094-2405279
Journal Article Type | Article |
---|---|
Acceptance Date | Apr 7, 2013 |
Online Publication Date | Jan 8, 2014 |
Publication Date | Jan 1, 2014 |
Deposit Date | Mar 19, 2012 |
Publicly Available Date | Mar 28, 2024 |
Journal | Duke Mathematical Journal |
Print ISSN | 0012-7094 |
Electronic ISSN | 1547-7398 |
Publisher | Duke University Press |
Peer Reviewed | Peer Reviewed |
Volume | 163 |
Issue | 1 |
Pages | 65-116 |
DOI | https://doi.org/10.1215/00127094-2405279 |
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