A π₁ obstruction to having finite index monodromy and an unusual subgroup of infinite index in \textrmMod(Σ_g)

2024/03/12 by Ishan Banerjee, Banerjee, Ishan
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2403.07280

openalex publication_date 2024/03/12 · openalex created_date 2024/03/14 · openalex updated_date 2026/07/28

Abstract

Let X be an algebraic surface with L an ample line bundle on X. Let Γ(X, L) be the geometric monodromy group associated to family of nonsingular curves in X that are zero loci of sections of L. We provide obstructions to Γ(X, L) being finite index in the mapping class group. We also show that for any k ≥ 0, the image of monodromy is finite index in appropriate subgroups of the quotient of the mapping class group by the kth term of the Johnson filtration assuming that L is sufficiently ample. This enables us to construct several subgroups of the mapping class group with unusual properties, in some cases providing the first examples of subgroups with those properties.

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