Minimal Cohomology Classes and Jacobians

dc.creatorDebarre, Olivier
dc.date1993-01-06
dc.date1993-11-08
dc.date.accessioned2026-07-07T08:57:40Z
dc.date.available2026-07-07T08:57:40Z
dc.descriptionWe show that on the Jacobian $(JC,θ)$ of a smooth curve $C$ of genus $g$, any effective cycle in $JC$ with cohomology class $θ^d/d!$ is a translate of $W_{g-d}(C)$ or $-W_{g-d}(C)$. We then use this result to prove that for $1<d<g$, the Jacobian locus (\resp the locus of intermediate Jacobians of cubic threefolds) is an irreducible component of the set of principally polarized abelian varieties of dimension $g$ for which $θ^d/d!$ (\resp $θ^3/3!$) is the class of an effective algebraic cycle. Moreover, on the intermediate Jacobian of a generic cubic threefold, $θ^2/2!$ is not the class of an effective algebraic cycle.
dc.description13 pages, Plain Tex 1.2
dc.identifierhttps://arxiv.org/abs/alg-geom/9301002
dc.identifierhttp://arxiv.org/abs/alg-geom/9301002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/147056
dc.subjectAlgebraic Geometry
dc.titleMinimal Cohomology Classes and Jacobians
dc.typetext

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