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Lecture Notes in Mathematics

Intersections of Hirzebruch–Zagier Divisors and CM Cycles

Authors: Howard, Benjamin, Yang, Tonghai

  • Develops new methods in explicit arithmetic intersection theory
  • Develops new techniques for the study of Shimura varieties and automorphic forms, central objects in modern number theory
  • Proves new cases of conjectures of S. Kudla
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  • ISBN 978-3-642-23979-3
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About this book

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.

Reviews

From the reviews:

“The reviewer recommends this beautiful monograph to anyone interested in the circle of conjecture proposed by Kudla et al., particularly from the point of view of arithmetic geometry. The work contains many useful references and intricate proofs that do not appear elsewhere, and is likely to be extremely useful to future progress in the area.” (Jeanine Van Order, Zentralblatt MATH, Vol. 1238, 2012)


Table of contents (6 chapters)

Buy this book

eBook 29,74 €
price for Spain (gross)
  • ISBN 978-3-642-23979-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 36,35 €
price for Spain (gross)
  • ISBN 978-3-642-23978-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Intersections of Hirzebruch–Zagier Divisors and CM Cycles
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2041
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-23979-3
DOI
10.1007/978-3-642-23979-3
Softcover ISBN
978-3-642-23978-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 140
Topics