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Intersections of Hirzebruch-Zagier Divisors and CM Cycles (Lecture Notes in Mathematics)
Howard, Benjamin, Yang, Tonghai
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Description for Intersections of Hirzebruch-Zagier Divisors and CM Cycles (Lecture Notes in Mathematics)
Paperback.
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 ... Read more
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 ... Read more
Product Details
Format
Paperback
Publication date
2012
Publisher
Springer
Condition
New
Number of Pages
140
Place of Publication
Berlin, Germany
ISBN
9783642239786
SKU
V9783642239786
Shipping Time
Usually ships in 15 to 20 working days
Ref
99-15
Reviews for Intersections of Hirzebruch-Zagier Divisors and CM Cycles (Lecture Notes in Mathematics)
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 ... Read more