A degree doubling formula for braid monodromies and Lefschetz pencils

2006/04/28 by Denis Auroux, Ludmil Katzarkov, Auroux, Denis +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.math/0605001

openalex publication_date 2006/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Every compact symplectic 4-manifold can be realized as a branched cover of the complex projective plane branched along a symplectic curve with cusp and node singularities; the covering map is induced by a triple of sections of a "very ample" line bundle. In this paper, we give an explicit formula describing the behavior of the braid monodromy invariants of the branch curve upon degree doubling of the linear system (from a very ample bundle L^k to L^2k). As a consequence, we derive a similar degree doubling formula for the mapping class group monodromy of Donaldson's symplectic Lefschetz pencils.

Citations

• Symplectic maps to projective spaces and symplectic invariants

Cited by

• Lefschetz pencils on a complex projective plane from a topological viewpoint

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