Borcherds Products on O(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 $(SL) 2(R)$. 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.

Riassunto

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.

Dettagli sul prodotto

• Autori: Jan H. Bruinier, Jan H Bruinier
• Editore: Springer, Berlin
• Lingue: Inglese
• Contenuto: Libro
• Forma del prodotto: Tascabile
• Data pubblicazione: 01.01.2007
• Categoria: Scienze naturali, medicina, informatica, tecnica > Matematica > Aritmetica, algebra
• EAN: 9783540433200
• ISBN: 978-3-540-43320-0
• Numero di pagine: 152
• Peso (della confezione): 250 g
• Serie: Lecture Notes in Mathematics > 1780; Lecture Notes in Mathematics
• Categorie: Algebra, B, Algebraische Geometrie, Mathematics and Statistics, Algebraic Geometry, Field Theory and Polynomials, Field theory (Physics), orthogonal group