Intersections of Hirzebruch-Zagier Divisors & CM Cycles

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Intersections of Hirzebruch-Zagier Divisors & CM Cycles By Benjamin Howard, Tonghai Yang
2012 | 152 Pages | ISBN: 3642239781 | PDF | 1 MB


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 & 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, & the special cycles are complex multiplication points & the Hirzebruch-Zagier divisors. By developing new techniques in deformation theory, the authors successfully compute the Arakelov intersection multiplicities of these divisors, & show that they agree with the Fourier coefficients of derivatives of Eisenstein series.
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Tags: Intersections, Hirzebruch, Divisors, Cycles

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