Borcherds Products on O(2,l) and Chern Classes of Heegner Divisors
Edition: 1 edition
Publisher: Springer
Published: May 31, 2002
Language: eng
Format: Paperback
Number of pages: 152
ISBN-13: 9783540433200
Subjects: Analytic number theory; Algebraic Geometry; Theory Of Numbers; Mathematics; Science/Mathematics; Algebra - General; Geometry - Algebraic; Number Theory; Automorphic form; Chern class; Heegner divisor; Mathematics / Algebra / General; Mathematics / Number Theory; Mathematics : Algebra - General; Mathematics : Geometry - Algebraic; Weil representation; Algebraic cycles; Chern classes; Forms, Modular; Picard groups; Series, Theta
Description: 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.
Notes: Lecture Notes in Mathematics