Arnold's seminar
December 18, 2001
  
Resolution of corank 1 stable singularities
of a generic front

V.D.Sedykh

New conditions of the coexistence of corank 1 stable singularities
of a generic front are found. Namely, if the boundary $\Gamma$ of a
connected component of the complement to a front is compact and
has only singularities $A_{\mu_1}+\dots+A_{\mu_m}$ with odd multiplicities
$\mu_1,\dots,\mu_m$, then the Euler number of any odd-dimensional
manifold ${\cal A}$ of singularities of the hypersurface $\Gamma$ is
equal to the sum of expressions every of which is nontrivial linear
combination of Euler numbers of even-dimensional manifolds of its
singularities having the same codimension greater than codimension
of the manifold ${\cal A}$. The coefficients of these combinations
are universal, i.e. they do not depend on a front, on the ambient space,
and on hypersurface $\Gamma$. For a proof we define a resolution
of corank 1 stable singularities of a generic front.