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Intersections of Hirzebruch–Zagier Divisors and CM Cycles

  • Benjamin Howard
  • Tonghai Yang

Part of the Lecture Notes in Mathematics book series (LNM, volume 2041)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Benjamin Howard, Tonghai Yang
    Pages 1-9
  3. Benjamin Howard, Tonghai Yang
    Pages 11-24
  4. Benjamin Howard, Tonghai Yang
    Pages 25-41
  5. Benjamin Howard, Tonghai Yang
    Pages 43-63
  6. Benjamin Howard, Tonghai Yang
    Pages 65-84
  7. Benjamin Howard, Tonghai Yang
    Pages 85-133
  8. Back Matter
    Pages 135-140

About this book

Introduction

This monograph treats one case of a series of conjectures by S. Kudla, whose goal is to show that Fourier of Eisenstein series encode information about the Arakelov intersection theory of special cycles on Shimura varieties of orthogonal and unitary type. Here, the Eisenstein series is a Hilbert modular form of weight one over a real quadratic field, the Shimura variety is a classical Hilbert modular surface, and the special cycles are complex multiplication points and the Hirzebruch–Zagier divisors. By developing new techniques in deformation theory, the authors successfully compute the Arakelov intersection multiplicities of these divisors, and show that they agree with the Fourier coefficients of derivatives of Eisenstein series.

Keywords

11-XX Arakelov geometry Hilbert modular surfaces arithmetic intersection theory automorphic forms

Authors and affiliations

  • Benjamin Howard
    • 1
  • Tonghai Yang
    • 2
  1. 1.Department of MathematicsBoston CollegeChestnut HillUSA
  2. 2.Department of MathematicsUniversity of Wisconsin, MadisonMadisonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-23979-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-23978-6
  • Online ISBN 978-3-642-23979-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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