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Go forward to Implementation Aspects of the Resolution Algorithm:
Blowing Up Along Nontrivial Centers
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Go backward to Category Theory (talk 2) Go up to Winter Semester '98 Go forward to Implementation Aspects of the Resolution Algorithm: Blowing Up Along Nontrivial Centers |
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Talker: Gábor Bodnár
The resolution algorithm needs to compute coefficient ideals, usually several times consecutively, until it arrives to a situation in which it can perform a blowing up operation to forward the resolution process. This causes enormous increase in the exponents of the generators of the ideals (embedded factorials). The problem can be overcome by developing a new way representing polynomial ideals, where each generator gets a rational weight. The new "generalized ideals" need, of course, new ways of computing singular locus, order, and transform along blowing ups.
In this talk we build up the first steps of the theory of "generalized ideals" and present the new computation methods for the tasks mentioned above.