In this paper we establish the relationships between theta functions of arbitrary order and their derivatives. We generalize our previous work [4] and prove that for any n > 1 the map sending an abelian variety to the set of Gauss images of its points of order 2n is an embedding into an appropriate Grassmannian (note that for n = 1 we only got generic injectivity in [4]). We further discuss the generalizations of Jacobi's derivative formula for any dimension and any order.
Theta functions of arbitrary order and their derivatives / Samuel, Grushevsky; SALVATI MANNI, Riccardo. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - STAMPA. - 590:590(2006), pp. 31-43. [10.1515/crelle.2006.002]
Theta functions of arbitrary order and their derivatives
SALVATI MANNI, Riccardo
2006
Abstract
In this paper we establish the relationships between theta functions of arbitrary order and their derivatives. We generalize our previous work [4] and prove that for any n > 1 the map sending an abelian variety to the set of Gauss images of its points of order 2n is an embedding into an appropriate Grassmannian (note that for n = 1 we only got generic injectivity in [4]). We further discuss the generalizations of Jacobi's derivative formula for any dimension and any order.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
