Minimal Cohomology Classes and Jacobians
| dc.creator | Debarre, Olivier | |
| dc.date | 1993-01-06 | |
| dc.date | 1993-11-08 | |
| dc.date.accessioned | 2026-07-07T08:57:40Z | |
| dc.date.available | 2026-07-07T08:57:40Z | |
| dc.description | We 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.description | 13 pages, Plain Tex 1.2 | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9301002 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9301002 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147056 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Minimal Cohomology Classes and Jacobians | |
| dc.type | text |