Vanishing cycles, the generalized Hodge Conjecture and Gröbner bases
| dc.creator | Shimada, Ichiro | |
| dc.date | 2003-11-12 | |
| dc.date.accessioned | 2026-07-07T05:02:48Z | |
| dc.date.available | 2026-07-07T05:02:48Z | |
| dc.description | Let $X$ be a general complete intersection of a given multi-degree in a complex projective space. Suppose that the anti-canonical line bundle of $X$ is ample. Using the cylinder homomorphism associated with the family of complete intersections contained in $X$, we prove that the vanishing cycles in the middle homology group of $X$ are represented by topological cycles whose support is contained in a proper Zariski closed subset $T\subset X$ of certain codimension. In some cases, we can find such a Zariski closed subset $T$ with codimension equal to the upper bound obtained from the Hodge structure of the middle cohomology group of $X$ by means of Gröbner bases. Hence a consequence of the generalized Hodge conjecture is verified in these cases. | |
| dc.description | 30pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0311180 | |
| dc.identifier | http://arxiv.org/abs/math/0311180 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69154 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C30, 14M10 | |
| dc.title | Vanishing cycles, the generalized Hodge Conjecture and Gröbner bases | |
| dc.type | text |