Séminaire de Géométrie Tropicale
Mercredi 9 septembre 2015 16h15 salle 1525-502
Geography of plane sextics
Résumé :
I will discuss the equisinguar deformation classification of
complex plane projective curves of degree 6 (sextics), with an
emphasis on those with simple singularities only. Thanks to the
close relation to $K3$-surfaces, the problem is easily reduced to
the arithmetics of integral lattices. The novelty of our approach
is a systematic usage of the Miranda-Morrison results concerning
the discriminants of indefinite lattices. To illustrate the power
of this approach, we also solve several related geometric problems,
such as the monodromy groups, adjacency of the strata, the
existence of real curves, etc. Some of our findings are quite
unexpected; the most interesting one is probably a real
equisingular stratum containing no real curves.
As a by-product, we almost complete the computation of the
fundamental groups of the complements of irreducible sextics.
This is a joint work with Ayşegül Akyol.