Monodromy of a family of hypersurfaces

2008/03/11 by Vincenzo Di Gennaro, Di Gennaro, Vincenzo, Davide Franco +1
Mathematics · #14B05 #14C20 #14C21 #14C25 #14D05 #14M10 #32S55 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.0803.1627

openalex publication_date 2008/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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≥ δ+1, and assume the general divisor X ∈ |H⁰(Y,\ic_Z,Y(d))| is smooth. Denote by H^m(X;\mathbb Q)_{⊥ Z}^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)_{⊥ Z}^van for the family of smooth divisors X ∈ |H⁰(Y,\ic_Z,Y(d))| is irreducible.

Related

• Monodromy of a family of hypersurfaces containing a given subvariety
• Monodromie d'une famille d'hypersurfaces
• Primitive cohomology and the tube mapping
• Monodromy representations of p-adic differential equations in families
• Low degree subvarieties of universal hypersurfaces