Higgs line bundles, Green-Lazarsfeld sets,\\and maps of K\"ahler manifolds to curves
Higgs line bundles, Green-Lazarsfeld sets,\\and maps of K\"ahler manifolds to curves
Let X be a compact Kähler manifold. The set $\operatorname {char}(X)$ of one-dimensional complex valued characters of the fundamental group of X forms an algebraic group. Consider the subset of $\operatorname {char}(X)$ consisting of those characters for which the corresponding local system has nontrivial cohomology in a given degree d. …