Monodromy of a family of hypersurfaces
| dc.creator | Di Gennaro, Vincenzo | |
| dc.creator | Franco, Davide | |
| dc.date | 2008-03-11 | |
| dc.date | 2009-04-28 | |
| dc.date.accessioned | 2026-07-07T13:08:35Z | |
| dc.date.available | 2026-07-07T13:08:35Z | |
| dc.description | Let $Y$ be an $(m+1)$-dimensional irreducible smooth complex projective variety embedded in a projective space. Let $Z$ be a closed subscheme of $Y$, and $δ$ be a positive integer such that $\mathcal I_{Z,Y}(δ)$ is generated by global sections. Fix an integer $d\geq δ+1$, and assume the general divisor $X \in |H^0(Y,\ic_{Z,Y}(d))|$ is smooth. Denote by $H^m(X;\mathbb Q)_{\perp Z}^{\text{van}}$ the quotient of $H^m(X;\mathbb Q)$ by the cohomology of $Y$ and also by the cycle classes of the irreducible components of dimension $m$ of $Z$. In the present paper we prove that the monodromy representation on $H^m(X;\mathbb Q)_{\perp Z}^{\text{van}}$ for the family of smooth divisors $X \in |H^0(Y,\ic_{Z,Y}(d))|$ is irreducible. | |
| dc.description | 13 pages, to appear on Ann. Scient. Ec. Norm. Sup | |
| dc.identifier | https://arxiv.org/abs/0803.1627 | |
| dc.identifier | http://arxiv.org/abs/0803.1627 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228466 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14B05; 14C20; 14C21; 14C25; 14D05; 14M10; 32S55 | |
| dc.title | Monodromy of a family of hypersurfaces | |
| dc.type | text |