Intersections of Hirzebruch-Zagier Divisors and CM Cycles
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.
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Intersections of Hirzebruch-Zagier Divisors and CM Cycles
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.
49.95 In Stock
Intersections of Hirzebruch-Zagier Divisors and CM Cycles

Intersections of Hirzebruch-Zagier Divisors and CM Cycles

by Benjamin Howard, Tonghai Yang
Intersections of Hirzebruch-Zagier Divisors and CM Cycles

Intersections of Hirzebruch-Zagier Divisors and CM Cycles

by Benjamin Howard, Tonghai Yang

Paperback(2012)

$49.95 
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Overview

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.

Product Details

ISBN-13: 9783642239786
Publisher: Springer Berlin Heidelberg
Publication date: 01/05/2012
Series: Lecture Notes in Mathematics , #2041
Edition description: 2012
Pages: 140
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1. Introduction.- 2. Linear Algebra.- 3. Moduli Spaces of Abelian Surfaces.- 4. Eisenstein Series.- 5. The Main Results.- 6. Local Calculations.

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