Moscow--Petersburg seminar on low-dimensional mathematics
SPb, PDMI, 07.06.2002, 16:00--17:45, room 311

I.Itenberg
Around the Ragsdale conjecture

The first part of Hilbert's 16-th problem is devoted to the
topology of real algebraic varieties, and more precisely, to the
topology of algebraic curves in the projective plane RP^2
and algebraic surfaces in the $3$-dimensional projective space
RP^3. We discuss recent developments in the subject that
are related to the {\it combinatorial patchworking}. This
construction is a particular case of the Viro method. The
combinatorial patchworking gives a possibility to construct real
algebraic varieties in a simple combinatorial way: one can
patchwork them from pieces which essentially are hyperplanes. The
applications of the combinatorial patchworking presented in the
talk are concentrated around the Ragsdale conjecture.