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A projective algebraic surface which is homeomorphic to a ruled surface over a curve of genus $gge 1$ is itself a ruled surface over a curve of genus $g$. In this note, we prove the analogous result for projective algebraic manifolds of dimension 4 in case $gge 2$.
If $M$ is a compact 3-manifold whose first betti number is 1, and $N$ is a compact 3-manifold such that $pi_1N$ and $pi_1M$ have the same finite quotients, then $M$ fibres over the circle if and only if $N$ does. We prove that groups of the form $F_2
Let $X$ be a smooth projective curve over the complex numbers. To every representation $rhocolon GL(r)lra GL(V)$ of the complex general linear group on the finite dimensional complex vector space $V$ which satisfies the assumption that there be an in
Let $G$ be a reductive group, and let $X$ be an algebraic curve over an algebraically closed field $k$ with positive characteristic. We prove a version of nonabelian Hodge correspondence for $G$-local systems over $X$ and $G$-Higgs bundles over the F
In this paper, we adapt the differential signature construction to the equivalence problem for complex plane algebraic curves under the actions of the projective group and its subgroups. Given an action of a group $G$, a signature map assigns to a pl
Let $S$ be a Riemann surface obtained by deleting a finite number of points, called cusps, from a compact Riemann surface. Let $rho: pi_1(S)to Sl(n, mathbb{C})$ be a semisimple linear representation of $pi_1(S)$ which is unipotent near the cusps. We