Sur les varietes de Hodge
| dc.creator | Otwinowska, Ania | |
| dc.date | 2004-01-09 | |
| dc.date.accessioned | 2026-07-07T05:04:27Z | |
| dc.date.available | 2026-07-07T05:04:27Z | |
| dc.description | Let $Y$ be a smooth complex projective variety of dimension $N+1$, $L$ an invertible sufficiently ample sheaf, $X\in |L|$ a smooth hypersurface and $λ\in F^kH^N(X,C)$ a vanishing cohomology class, where $F^{*}$ is the Hodge filtration and $k\in\{1,...,[N/2]\}$. Assume that $L$ is sufficiently ample and that the codimension in $|L|$ of the Hodge variety associated to $λ$ (locally defined as the locus where the image of $λ$ by flat transport over $|L|$ remains in $F^k$) is sufficiently small. I show that this forces $N$ to be even and $k=[N/2]$, and that the class $λ$ is a linear combination with complex coefficients of classes of algebraic subvarieties of $X$ of small degree. As a corollary, I obtain that the components of smallest codimensions of the Noether-Lefschetz locus are spanned by classes of algebraic subvarieties as predicted by Hodge conjecture. The proof relies on an algebraic description of the infinitesimal neighboorghood of the Noether-Lefschetz locus at any order and on a (global) monodromy result. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0401092 | |
| dc.identifier | http://arxiv.org/abs/math/0401092 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69811 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C30, 14C25 | |
| dc.title | Sur les varietes de Hodge | |
| dc.type | text |