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EnglishIn 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.
http://hdl.handle.net/11573/19419| Titolo: | Theta functions of arbitrary order and their derivatives |
| Autori interni: | SALVATI MANNI, Riccardo |
| Data di pubblicazione: | 2006 |
| Rivista: | JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK |
| 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. |
| Handle: | http://hdl.handle.net/11573/19419 |
| Appare nelle tipologie: | 01.a Pubblicazione su Rivista |
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