Intersections of Hirzebruch-Zagier Divisors and CM Cycles

2012
ISBN: 978-3-642-23978-6
Verlag: Springer

Buch, Englisch, Band 2041, 140 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 242 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Yang, Tonghai

Howard, Benjamin

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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