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Mathematics - Algebra | Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors

Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors

Series: Lecture Notes in Mathematics, Vol. 1780

Bruinier, Jan H.

2002, VIII, 156 p.

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  • About this book

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.

Content Level » Research

Keywords » Automorphic form - Chern class - Heegner divisor - Lattice - Weil representation - modular form - orthogonal group

Related subjects » Algebra

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