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

• Main Author: Bruinier, Jan H. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1780
• Subjects: Algebra.; Field theory (Physics).; Algebraic geometry.; Field Theory and Polynomials.; Algebraic Geometry.
• Physical Description: VIII, 156 p. online resource.
• ISBN: 9783540458722
• ISSN: 0075-8434 ;
• DOI: 10.1007/b83278

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.