Name: Santiago Encinas
Title: Algorithmic Equiresolution
Abstract:
Given an algorithm of resolution of singularities satisfying
certain conditions, natural notions of
simultaneous algorithmic resolution, or equiresolution, for
families of embedded schemes (parametrized by a reduced scheme $T$)
are proposed. These conditions are equivalent.
Something similar is done for families of sheaves of ideals, here
the goal is algorithmic simultaneous principalization. A
consequence is that given a family of embedded schemes over a
reduced $T$, this parameter scheme can be naturally expressed as a
disjoint union of locally closed sets $T_{j}$, such that the
induced family on each part $T_{j}$ is
equisolvable. In particular, this can be applied to the Hilbert
scheme of a smooth projective variety; in fact, our result shows that,
in characteristic zero, the underlying topological space of
any Hilbert scheme parametrizing embedded schemes
can be naturally stratified in equiresolvable families.