Details
| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 12 Jan 2024 |
Abstract
Keywords
- math.AG, math.CV, math.NT
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2024.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - Curves on powers of hyperelliptic Jacobians
AU - Schreieder, Stefan
AU - de Gaay Fortman, Atahualpa Olivier Daniel
N1 - 52 pages
PY - 2024/1/12
Y1 - 2024/1/12
N2 - For a curve of genus at least four which is either very general or very general hyperelliptic, we classify all ways in which a power of its Jacobian can be isogenous to a product of Jacobians of curves. As an application, we show that, for a very general principally polarized abelian variety of dimension at least four, or the intermediate Jacobian of a very general cubic threefold, no power is isogenous to a product of Jacobians of curves. This confirms some cases of the Coleman-Oort conjecture. We further deduce from our results some progress on the question whether the integral Hodge conjecture fails for such abelian varieties.
AB - For a curve of genus at least four which is either very general or very general hyperelliptic, we classify all ways in which a power of its Jacobian can be isogenous to a product of Jacobians of curves. As an application, we show that, for a very general principally polarized abelian variety of dimension at least four, or the intermediate Jacobian of a very general cubic threefold, no power is isogenous to a product of Jacobians of curves. This confirms some cases of the Coleman-Oort conjecture. We further deduce from our results some progress on the question whether the integral Hodge conjecture fails for such abelian varieties.
KW - math.AG
KW - math.CV
KW - math.NT
M3 - Preprint
BT - Curves on powers of hyperelliptic Jacobians
ER -