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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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Sum total of downloads: 31
| 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). | |
| License of this version: | CC BY 4.0 Unported |
| Document Type: | Article |
| Publishing status: | publishedVersion |
| Issue Date: | 2022 |
| Appears in Collections: | Fakultät für Mathematik und Physik |
distribution of downloads over the selected time period:
downloads by country:
| pos. | country | downloads | ||
|---|---|---|---|---|
| total | perc. | |||
| 1 |  |
Germany | 14 | 45.16% |
| 2 |  |
United States | 9 | 29.03% |
| 3 |  |
China | 4 | 12.90% |
| 4 |  |
Taiwan | 1 | 3.23% |
| 5 |  |
Thailand | 1 | 3.23% |
| 6 |  |
Ireland | 1 | 3.23% |
| 7 |  |
Spain | 1 | 3.23% |
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