Recently, I constructed a surface of degree 7 in real 3-space admitting 99 ordinary double points (see my paper on arXiv.org: math.AG/0409348) while writing my Ph.D. thesis under the direction of Duco van Straten.
This improves the lower bound on the maximum number of nodes a septic can have by 6 (cf. our page on surfaces with many nodes), s.t. we now have (together with Varchenko's - or Givental's - upper bound):
Moreover, all the singularities are real, s.t. one can generate pictures of it using the great program surf, written by St. Endraß et al.
Here is a first view on the "inner part" of the 99-nodal septic:
You can also download a low-quality mpg-movie showing the surface by
clicking on the small gif-animation (1.5 MB) below.
It zooms in and out to allow you to see both the whole surface and the
inner part:
We used the great program Singular to obtain the result, although it can be checked by hand, once it has been found.
On a page on the construction of the septic with 99 nodes, I give some information and images in order to illustrate the construction. This page will be updated frequently in the near future, because there are still some images and movies to produce...
--- more information on the construction of the septic with 99 nodes
Please contact me, if you have any comments or questions,
Oliver Labs
mail: oliver@AlgebraicSurface.net
home: www.AlgebraicSurface.net
or
Algebraic Geometry Group Mainz, Germany