Geometriae Dedicata

We classify projective symmetries of irreducible plane sextics with simple singularities which are stable under equivariant deformations. We also outline a connection between order 2 stable symmetries and maximal trigonal curves.

We classify homogeneous surfaces in real and complex affine three-space. This is achieved by choosing affine coordinates so that the surface is defined by a function whose Taylor series is in a preferred normal form.

In this paper NC-groups (i.e. finite groups G, in which for every Sylow p-subgroup P of G, N G(Z(P))=C G(Z(P)) are studied. Mainly the Authors give a way to construct solvable NC-groups with arbitrarely large fitting length and trivial center. Further some results about nonsolvable NC-groups are given.

Given a closed surface $$S$$ of genus at least 2, we compare the symplectic structure of Taubes’ moduli space of minimal hyperbolic germs with the Goldman symplectic structure on the character variety $${\fancyscript{X}}(S, { PSL}(2,{\mathbb {C}}))$$ and the affine cotangent symplectic structure on the space of complex projective structures $${\fancyscript{CP}}(S)$$ given by the Schwarzian parametrization. This is done in restriction to the moduli space of almost-Fuchsian structures by involving a notion of renormalized volume, used to relate the geometry of a minimal surface in a hyperbolic 3-manifold to the geometry of its ideal conformal boundary.

We prove that simply connected open manifolds of bounded geometry, linear growth and sublinear filling growth (e.g. finite filling area) are simply connected at infinity.