dc.identifier.uri |
http://dx.doi.org/10.15488/13027 |
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dc.identifier.uri |
https://www.repo.uni-hannover.de/handle/123456789/13131 |
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dc.contributor.author |
Alexandrou, Theodosis
|
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dc.date.accessioned |
2022-11-15T08:45:58Z |
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dc.date.available |
2022-11-15T08:45:58Z |
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dc.date.issued |
2022 |
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dc.identifier.citation |
Alexandrou, T.: The generic isogeny decomposition of the Prym Variety of a cyclic branched covering. In: Geometriae dedicata 216 (2022), Nr. 1, 2. DOI: https://doi.org/10.1007/s10711-021-00671-6 |
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dc.description.abstract |
Let f: S′⟶ S be a cyclic branched covering of smooth projective surfaces over C whose branch locus Δ ⊂ S is a smooth ample divisor. Pick a very ample complete linear system | H| on S, such that the polarized surface (S, | H|) is not a scroll nor has rational hyperplane sections. For the general member [C] ∈ | H| consider the μn-equivariant isogeny decomposition of the Prym variety Prym(C′/C) of the induced covering f: C′: = f- 1(C) ⟶ C: Prym(C′/C)∼∏d|n,d≠1Pd(C′/C).We show that for the very general member [C] ∈ | H| the isogeny component Pd(C′/ C) is μd-simple with Endμd(Pd(C′/C))≅Z[ζd]. In addition, for the non-ample case we reformulate the result by considering the identity component of the kernel of the map Pd(C′/C)⊂Jac(C′)⟶Alb(S′). © 2022, The Author(s). |
eng |
dc.language.iso |
eng |
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dc.publisher |
Dordrecht [u.a.] : Springer Science + Business Media B.V |
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dc.relation.ispartofseries |
Geometriae dedicata 216 (2022), Nr. 1 |
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dc.rights |
CC BY 4.0 Unported |
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dc.rights.uri |
https://creativecommons.org/licenses/by/4.0/ |
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dc.subject |
Cyclic covering |
eng |
dc.subject |
Isogeny decomposition |
eng |
dc.subject |
Jacobian variety |
eng |
dc.subject |
Prym variety |
eng |
dc.subject.ddc |
510 | Mathematik
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ger |
dc.title |
The generic isogeny decomposition of the Prym Variety of a cyclic branched covering |
eng |
dc.type |
Article |
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dc.type |
Text |
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dc.relation.essn |
1572-9168 |
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dc.relation.doi |
https://doi.org/10.1007/s10711-021-00671-6 |
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dc.bibliographicCitation.issue |
1 |
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dc.bibliographicCitation.volume |
216 |
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dc.bibliographicCitation.firstPage |
2 |
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dc.description.version |
publishedVersion |
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tib.accessRights |
frei zug�nglich |
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