Intersections of Hirzebruch-Zagier divisors and CM cycles
Author(s)
Bibliographic Information
Intersections of Hirzebruch-Zagier divisors and CM cycles
（Lecture notes in mathematics, 2041）
Springer, c2012
Available at 48 libraries
Note
Bibliography: p. 135-137
Includes index
Description and Table of Contents
Description
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.
Table of Contents
1. Introduction.- 2. Linear Algebra.- 3. Moduli Spaces of Abelian Surfaces.- 4. Eisenstein Series.- 5. The Main Results.- 6. Local Calculations.
by "Nielsen BookData"