Monodromy and vanishing cycles for complete intersection curves

2024/08/12 by Ishan Banerjee, Banerjee, Ishan, Nick Salter +1 · 2 citations
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric Topology (math.GT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2408.06479

openalex publication_date 2024/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the topological monodromy of every family of complete intersection curves. Like in the case of plane curves previously treated by the second-named author, we find the answer is given by the r-spin mapping class group associated to the maximal root of the adjoint line bundle. Our main innovation is a suite of tools for studying the monodromy of sections of a tensor product of very ample line bundles in terms of the monodromy of sections of the factors, allowing for an induction on (multi-)degree.

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• Monodromy and vanishing cycles for sufficiently ample linear systems on simply connected surfaces
• Fundamental groups of strata of abelian differentials of low codimension

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