11 citations · 14 across the 7 of their papers we have counts for
7 papers
A Quintic Hypersurface in $\PP^8(\CC)$ with Many Nodes
Oliver Schmidt, Oliver Labs, Duco van Straten
We construct a hypersurface of degree 5 in projective space $\PP^8(\CC)$ which contains exactly 23436 ordinary nodes and no further singularities. This limits the maximum number $μ…
Surfaces with Many Solitary Points
Erwan Brugalle Oliver Labs
It is classically known that a real cubic surface in the real projective 3-space cannot have more than one solitary point (locally given by x^2+y^2+z^2=0) whereas it can have up to…
The Casas-Alvero conjecture for infinitely many degrees
Hans-Christian Graf von Bothmer, Oliver Labs, Josef Schicho +1
Over a field of characteristic zero, it is clear that a polynomial of the form (X-a)^d has a non-trivial common factor with each of its d-1 first derivatives. The converse has been…
Real Line Arrangements and Surfaces with Many Real Nodes
Sonja Breske, Oliver Labs, Duco van Straten
A long standing question is if maximum number of nodes on a surface of degree in $\dP^3(\dC)$ can be achieved by a surface defined over the reals which has only real sin…
Dessins d'Enfants and Hypersurfaces with Many -Singularities
Oliver Labs
We show the existence of surfaces of degree in $\dP^3(\dC)$ with approximately singularities of type . The result is based on Chmu…
A Sextic with 35 Cusps
Oliver Labs
Recently, W. Barth and S. Rams discussed sextics with up to 30 -singularities (also called cusps) and their connection to coding theory [math.AG/0403018]. In the present paper…