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- W2055367295 abstract "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. This set is shown to be a union of finitely many components that are translates of algebraic subgroups of $operatorname {char}(X)$. When the degree d equals 1, it is shown that some of these components are pullbacks of the character varieties of curves under holomorphic maps. As a corollary, it is shown that the number of equivalence classes (under a natural equivalence relation) of holomorphic maps, with connected fibers, of X onto smooth curves of a fixed genus $> 1$ is a topological invariant of X. In fact it depends only on the fundamental group of X." @default.
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- W2055367295 date "1992-05-01" @default.
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- W2055367295 title "Higgs line bundles, Green-Lazarsfeld sets,and maps of Kahler manifolds to curves" @default.
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- W2055367295 doi "https://doi.org/10.1090/s0273-0979-1992-00283-5" @default.
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