A degeneration of compact Kähler manifolds gives rise to a monodromy action on the Betti moduli space H 1(X,G) = Hom(π1(X),G)/G over smooth fibres with a complex algebraic structure group G that is either abelian or reductive. Assume that the singularities of the central fibre are 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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics