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We prove that a reduced and irreducible algebraic surface in $mathbb{CP}^{3}$ containing infinitely many twistor lines cannot have odd degree. Then, exploiting the theory of quaternionic slice regularity and the normalization map of a surface, we give constructive existence results for even degrees.
We introduce and study (strict) Schottky G-bundles over a compact Riemann surface X, where G is a connected reductive algebraic group. Strict Schottky representations are shown to be related to branes in the moduli space of G-Higgs bundles over X, an
We describe the relation between supersymmetric sigma-models on hyperkahler manifolds, projective superspace, and twistor space. We review the essential aspects and present a coherent picture with a number of new results.
We give explicit pseudo-Anosov homeomorphisms with vanishing Sah-Arnoux-Fathi invariant. Any translation surface whose Veech group is commensurable to any of a large class of triangle groups is shown to have an affine pseudo-Anosov homeomorphism of t
In the early 1980s, S. T. Yau conjectured that any compact Riemannian three-manifold admits an infinite number of closed immersed minimal surfaces. We use min-max theory for the area functional to prove this conjecture in the positive Ricci curvature
We discuss the complex geometry of two complex five-dimensional Kahler manifolds which are homogeneous under the exceptional Lie group $G_2$. For one of these manifolds rigidity of the complex structure among all Kahlerian complex structures was prov