|
We have obtained the complete deformation classification of singular real plane
sextic curves with smooth real part, i.e., those without real singular points.
This was made possible due to the fact that, under the assumption, contrary
to the general case, the equivariant equisingular deformation type is determined
by the so-called real homological type in its most naN.ve sense, i.e., the
homological
information about the polarization, singularities, and real structure; one does not
need to compute the fundamental polyhedron of the group generated by reflections
and identify the classes of ovals therein. Should time permit, I will outline our
proof of this theorem.
As usual, this classification leads us to a number of observations, some of which
we have already managed to generalize. Thus, we have an ArnolŒd.Gudkov.Rokhlin
type congruence for close to maximal surfaces (and, hence, even degree curves) with
certain singularities. Another observation (which has not been quite understood
yet and may turn out K3-specific) is that the contraction of any empty oval of a
type I real scheme results in a bijection of the sets of deformation classes.
|