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EnglishIn this note we study the geometry of principally polarized abelian varieties (ppavs) with a vanishing theta-null (i.e. with a singular point of order two and even multiplicity lying on the theta divisor)-denote by theta(null) the locus of such ppavs. We describe the locus theta(g-1)(null) subset of theta(null) where this singularity is not an ordinary double point. By using theta function methods we first show theta(g-1)(null) not subset of theta(null) (this was shown in [4], see below for a discussion). We then show that theta(g-1)(null) is contained in the intersection theta(null) boolean AND N(0)(') of the two irreducible components of the Andreotti-Mayer N(0) = theta(null) + 2N(0)', and describe by using the geometry of the universal scheme of singularities of the theta divisor which components of this intersection are in theta(g-1)(null). Some of the intermediate results obtained along the way of our proof were concurrently obtained independently by C. Ciliberto and G. van der Geer in [3] and by R. de Jong in [5], version 2.
Singularities of the Theta Divisor at Points of Order Two / S., Grushevsky; SALVATI MANNI, Riccardo. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - 2007(2007), pp. 1-15. [10.1093/imrn/rnm045]
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| Titolo: | Singularities of the Theta Divisor at Points of Order Two | |
| Autori: | ||
| Data di pubblicazione: | 2007 | |
| Rivista: | ||
| Citazione: | Singularities of the Theta Divisor at Points of Order Two / S., Grushevsky; SALVATI MANNI, Riccardo. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - 2007(2007), pp. 1-15. [10.1093/imrn/rnm045] | |
| Handle: | http://hdl.handle.net/11573/20220 | |
| Appartiene alla tipologia: | 01a Articolo in rivista |
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