A degree doubling formula for braid monodromies and Lefschetz pencils

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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.
65 pages; revised version of a preprint that has been in limited circulation since 2000, with improved exposition

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Symplectic Geometry, Algebraic Geometry, Geometric Topology

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http://salesiana.dossiersoluciones.com/handle/123456789/112599

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0605001
 http://arxiv.org/abs/math/0605001

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arXiv