Generalized Thomas hyperplane sections and relations between vanishing cycles
| dc.creator | Saito, Morihiko | |
| dc.date | 2008-06-09 | |
| dc.date | 2008-09-29 | |
| dc.date.accessioned | 2026-07-07T10:05:35Z | |
| dc.date.available | 2026-07-07T10:05:35Z | |
| dc.description | As is remarked by B. Totaro, R. Thomas essentially proved that the Hodge conjecture is inductively equivalent to the existence of a hyperplane section, called a generalized Thomas hyperplane section, such that the restriction to it of a given primitive Hodge class does not vanish. We study the relations between the vanishing cycles in the cohomology of a general fiber, and show that each relation between the vanishing cycles of type (0,0) with unipotent monodromy around a singular hyperplane section defines a primitive Hodge class such that this singular hyperplane section is a generalized Thomas hyperplane section if and only if the pairing between a given primitive Hodge class and some of the constructed primitive Hodge classes does not vanish. This is a generalization of a construction by P. Griffiths. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0806.1461 | |
| dc.identifier | http://arxiv.org/abs/0806.1461 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170051 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32S40 | |
| dc.title | Generalized Thomas hyperplane sections and relations between vanishing cycles | |
| dc.type | text |