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Intersections of Hirzebruch–Zagier Divisors and CM Cycles [electronic resource] /by Benjamin Howard, Tonghai Yang.

by Howard, Benjamin [author.]; Yang, Tonghai [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lecture Notes in Mathematics: 2041Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.Description: VIII, 140p. online resource.ISBN: 9783642239793.Subject(s): Mathematics | Number theory | Mathematics | Number TheoryDDC classification: 512.7 Online resources: Click here to access online
Contents:
1. Introduction -- 2. Linear Algebra -- 3. Moduli Spaces of Abelian Surfaces -- 4. Eisenstein Series -- 5. The Main Results -- 6. Local Calculations.
In: Springer eBooksSummary: 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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1. Introduction -- 2. Linear Algebra -- 3. Moduli Spaces of Abelian Surfaces -- 4. Eisenstein Series -- 5. The Main Results -- 6. Local Calculations.

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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