Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

Space - Time Singularities and the Kähler Cone

We review recent results on the interplay between the five-dimensional spacetime and the internal manifold in Calabi-Yau compactifications of M-theory. Black string, black hole and domain wall solutions as well as Kasner type cosmologies cannot develop a naked singularity as long as the moduli take values inside the Kähler cone. String and M-theory provide mechanisms and effects which improve o...

Efficient Resolution of Singularities of Plane Curves

We give a new algorithm for resolving singularities of plane curves. The algorithm is polynomial time in the bit complexity model, does not require factorization, and works over Q or finite fields.

Deformations of Singularities of Plane Curves

In this paper we present some new results in the deformation theory of plane curve singularities. The methods rely on the study of analytic properties of linear non homogeneous ODE’s.

Eecient Resolution of Singularities of Plane Curves

We give a new algorithm for resolving singularities of plane curves. The algorithm is polynomial time in the bit complexity model, does not require factorization, and works over Q or nite elds.

Resolution of Singularities for Plane Curves