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]
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Titolo: | Theta functions of arbitrary order and their derivatives | |
Autori: | ||
Data di pubblicazione: | 2006 | |
Rivista: | ||
Citazione: | 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] | |
Handle: | http://hdl.handle.net/11573/19419 | |
Appartiene alla tipologia: | 01a Articolo in rivista |