123 research outputs found
A Simplified Game for Resolution of Singularities
We will describe a combinatorial game that models the problem of resolution
of singularities of algebraic varieties over a field of characteristic zero. By
giving a winning strategy for this game, we give another proof of the existence
of resolution
Counting projections of rational curves
Given two general rational curves of the same degree in two projective
spaces, one can ask whether there exists a third rational curve of the same
degree that projects to both of them. We show that, under suitable assumptions
on the degree of the curves and the dimensions of the two given ambient
projective spaces, the number of curves and projections fulfilling the
requirements is finite. Using standard techniques in intersection theory and
the Bott residue formula, we compute this number.Comment: 27 page
Self-motions of pentapods with linear platform
We give a full classification of all pentapods with linear platform
possessing a self-motion beside the trivial rotation about the platform. Recent
research necessitates a contemporary and accurate re-examination of old results
on this topic given by Darboux, Mannheim, Duporcq and Bricard, which also takes
the coincidence of platform anchor points into account. For our study we use
bond theory with respect to a novel kinematic mapping for pentapods with linear
platform, beside the method of singular-invariant leg-rearrangements. Based on
our results we design pentapods with linear platform, which have a simplified
direct kinematics concerning their number of (real) solutions.Comment: 28 pages, 5 figure
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