=ADD=
=reftype=
14
=number=
01-04
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2001/01-04.ps.gz
=year=
2001
=month=
01
=author=
Bodnar; Gabor
=title=
Algorithmic Resolution of Singularities
=abstract=
The problem of algorithmic resolution of singularities is to construct
a proper birational morphism from some nonsingular variety to a given
variety.  The problem is solvable if the base field is of
characteristic zero; in positive characteristic it is still open.  The
morphism and the nonsingular variety is constructed by composing well
chosen transformations (blowing ups) over the given variety.

In this thesis, relying on constructive proofs available in the
literature, we develop an algorithm for the resolution of
singularities of hypersurfaces over fields of zero characteristic.  We
also present several improvements of this algorithm, developing
advanced computational techniques for the subtasks of the resolution
process.  The thesis is accompanied by a full implementation of the
algorithm.

Finally, we solve a problem related to the main topic: the
construction of a blowing up which is isomorphic to the composition of
a given sequence of blowing ups.
=note=
PhD Thesis
=sponsor=
FWF P12662, SFB-P2 F1303