=ADD=
=reftype=
14
=number=
00-03
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2000/00-03.ps.gz
=year=
2000
=month=
01
=author=
Bodnar; Gabor + Schicho; Josef
=title=
Improvements of the Algorithm for Resolution of Singularities
=abstract=
This paper contains several improvements of Villmayor's algorithm
for the problem of resolution of singularities of hypersurfaces.
First, a condition is presented for avoiding superfluous
intermediate resolution problems to be generated (computation of
coefficient objects with respect to many hypersurfaces).  Then a new
representation of algebraic sets is developed to avoid rising the
generators of their vanishing ideals to extremely high powers.
Based on this improvement, a new representation of basic objects
(i.e. resolution problems) is introduced, enabling the algorithm to
exploit special structures appearing in them.  Finally, a technique
is presented for the efficient management of charts of the
describing atlas of blown up varieties.
=sponsor=
FWF project "Computation of Adjoints for Surfaces"
=end=