Borcherds products on 0(2,l) and Chern classes of Heegner divisors

Around 1994 R. Borcherds discovered a new type of meromorphic modular form on the orthogonal group $O(2,n)$. These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as multiplicative liftings of elliptic modular forms on $(SL)_2(R)$. T...

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Bibliographic Details
Main Author Bruinier, Jan H
Format eBook
LanguageEnglish
Published Springer 15.09.2006
SeriesLecture notes in mathematics
Subjects
Algebraic cycles
Chern classes
Forms, Modular
Picard groups
Series, Theta
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Summary:Around 1994 R. Borcherds discovered a new type of meromorphic modular form on the orthogonal group $O(2,n)$. These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as multiplicative liftings of elliptic modular forms on $(SL)_2(R)$. The fact that the zeros and poles of Borcherds products are explicitly given in terms of Heegner divisors makes them interesting for geometric and arithmetic applications. In the present text the Borcherds' construction is extended to Maass wave forms and is used to study the Chern classes of Heegner divisors. A converse theorem for the lifting is proved.
ISBN:3540433201
9783540433200