Campus Event Calendar
Event Entry
What and Who
Analysis of Square Free Algebraic Plane Curves
Michael Kerber
IMPRS
Talk
AG 1, AG 2, AG 3, AG 4, AG 5, SWS
AG Audience
English
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Date, Time and Location
Monday, 10 July 2006
08:30
330 Minutes
E1 4
024
Saarbrücken
Abstract
We give a solution for the transformation of an algebraic plane curve
into a combinatorial graph where edges correspond to x-monotone segments
of the curve (curve analysis). The approach is exact in the sense that
it preserves the topology of the curve.
By combining exact and approximated calculations, our algorithm improves
the state-of-the-art solutions without sacrifying exactness. Although
certain genericity conditions are used during the analysis, we do not
impose any condition on the input curve and can therefore handle all
sorts of degeneracy.
My talk concentrates on how (controlled) approximation can be used to
speed up the analysis under the assumption of a generic position for the
curve.Analysing algebraic plane curves means to deduce various geometric
properties, such as locating singularities, counting incident arcs etc.
My talk explains how genericity conditions simplify the curve analysis
and how to transfer this techniques to arbitrary algebraic curves.
into a combinatorial graph where edges correspond to x-monotone segments
of the curve (curve analysis). The approach is exact in the sense that
it preserves the topology of the curve.
By combining exact and approximated calculations, our algorithm improves
the state-of-the-art solutions without sacrifying exactness. Although
certain genericity conditions are used during the analysis, we do not
impose any condition on the input curve and can therefore handle all
sorts of degeneracy.
My talk concentrates on how (controlled) approximation can be used to
speed up the analysis under the assumption of a generic position for the
curve.Analysing algebraic plane curves means to deduce various geometric
properties, such as locating singularities, counting incident arcs etc.
My talk explains how genericity conditions simplify the curve analysis
and how to transfer this techniques to arbitrary algebraic curves.
Contact
Kerstin Kathy Meyer-Ross
226
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Jennifer Gerling, 07/07/2006 12:27
Jennifer Gerling, 07/03/2006 09:26
Jennifer Gerling, 06/26/2006 12:00 -- Created document.
Jennifer Gerling, 07/03/2006 09:26
Jennifer Gerling, 06/26/2006 12:00 -- Created document.