A septic with 99 real nodes
About the computation of the signature of surface singularities z N + g(x, y) = 0
In this article we describe our experiences with a parallel Singular implementation of the signature of a surface singularity defined by z N + g(x; y) = 0.
Algorithms for the computation of moduli spaces for semiquasihomogeneous singularities.
We present algorithms and their implementation in the computer algebra system Singular 2.0 for the computation of equations for moduli spaces for semiquasihomogeneous singularities w.r.t. right equivalence. In addition, we describe the structure of the stabilizer group of Brieskorn-Pham singularities.
An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity
Let be a germ of a complete intersection variety in , , having an isolated singularity at and be the germ of a holomorphic vector field having an isolated zero at and tangent to . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of is also isolated in the ambient space we give a formula for the homological index in terms of local linear algebra.
An algorithmic criterion for basicness in dimension 2.
Approximate implicitization of parametric curves using cubic algebraic splines.
Counting lines on surfaces
This paper deals with surfaces with many lines. It is well-known that a cubic contains of them and that the maximal number for a quartic is . In higher degree the question remains open. Here we study classical and new constructions of surfaces with high number of lines. We obtain a symmetric octic with lines, and give examples of surfaces of degree containing a sequence of skew lines.
Feasibility Testing for Systems of Real Quadratic Equations.
Geometrické modelování – od historie k současnosti a budoucnosti
Higher degree Galois covers of .
Kähler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces
We determine all anticanonically embedded quasi smooth log del Pezzo surfaces in weighted projective 3-spaces. Many of these admit a Kähler-Einstein metric and most of them do not have tigers.
Modular deformations and space curve singularities.
We investigate different concepts of modular deformations of germs of isolated singularities (infinitesimal, Artinian, formal). An obstruction calculus based on the graded Lie algebra structure of the tangent cohomology for modular dcformations is introduced. As the main result the characterisation of the maximal infinitesimally modular subgerm of the miniversal family as flattening stratum of the relative Tjurina module is extended from ICIS to space curve singularities.
Real quartic surfaces containing 16 skew lines.
Sur les surfaces algébriques
The dual of the invariant quintic.
The fundamental group for the complement of Cayley's singularities.
The fundamental group of a Galois cover of .
Théorèmes sur les coniques et sur les surfaces de second ordre
Théorie des indices