Mathematics – Symplectic Geometry
Scientific paper
2006-04-28
Mathematics
Symplectic Geometry
65 pages; revised version of a preprint that has been in limited circulation since 2000, with improved exposition
Scientific paper
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.
Auroux Denis
Katzarkov Ludmil
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