Details
| Original language | English |
|---|---|
| Article number | 2 |
| Journal | GEOMETRIAE DEDICATA |
| Volume | 216 |
| Issue number | 1 |
| Publication status | Published - 3 Jan 2022 |
| Externally published | Yes |
Abstract
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′).
Keywords
- math.AG, Isogeny decomposition, Jacobian variety, Prym variety, Cyclic covering
ASJC Scopus subject areas
- Mathematics(all)
- Geometry and Topology
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In: GEOMETRIAE DEDICATA, Vol. 216, No. 1, 2, 03.01.2022.
Research output: Contribution to journal › Article › Research
}
TY - JOUR
T1 - The Generic Isogeny Decomposition of the Prym Variety of a Cyclic Branched Covering
AU - Alexandrou, Theodosis
N1 - Funding information: The author thanks his advisor Professor Dr. Daniel Huybrechts and Dr. Gebhard Martin for helpful discussions on the topics of this note, which are parts of the author’s Master thesis, as well as for corrections.
PY - 2022/1/3
Y1 - 2022/1/3
N2 - 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′).
AB - 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′).
KW - math.AG
KW - Isogeny decomposition
KW - Jacobian variety
KW - Prym variety
KW - Cyclic covering
UR - http://www.scopus.com/inward/record.url?scp=85122266842&partnerID=8YFLogxK
U2 - 10.1007/s10711-021-00671-6
DO - 10.1007/s10711-021-00671-6
M3 - Article
VL - 216
JO - GEOMETRIAE DEDICATA
JF - GEOMETRIAE DEDICATA
SN - 0046-5755
IS - 1
M1 - 2
ER -