Cookies

We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.


Durham Research Online
You are in:

The geometric theta correspondence for Hilbert modular surfaces.

Funke, Jens and Millson, John (2014) 'The geometric theta correspondence for Hilbert modular surfaces.', Duke mathematical journal., 163 (1). pp. 65-116.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Download PDF
(951Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1215/00127094-2405279
Date accepted:07 April 2013
Date deposited:21 December 2013
Date of first online publication:08 January 2014
Date first made open access:08 January 2014

Save or Share this output

Export:
Export
Look up in GoogleScholar