Dehn twists and invariant classes

Details Dehn twists and invariant classes Dehn twists and invariant classes

2009-01-18

arxiv.org/abs/0901.2692v2

Mathematics

Algebraic Geometry

Minor change in terminology, correcting of a sentence in abstract and some typographic corrections

Scientific paper

A degeneration of compact Kaehler manifolds gives rise to a monodromy action on Betti moduli space H^1(X, G) = Hom(\pi_1(X),G)/G over smooth fibres with a complex algebraic structure group G being either abelian or reductive. Assume that the singularities of the central fibre is of normal crossing. When G = C, the invariant cohomology classes arise from the global classes. This is no longer true in general. In this paper, we produce large families of locally invariant classes that do not arise from global ones for reductive G. These examples exist even when G is abelian, as long as G contains multiple torsion points. Finally, for general G, we make a new conjecture on local invariant classes and produce some suggestive examples.

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