6,115 research outputs found
Partial Degree Formulae for Plane Offset Curves
In this paper we present several formulae for computing the partial degrees
of the defining polynomial of the offset curve to an irreducible affine plane
curve given implicitly, and we see how these formulae particularize to the case
of rational curves. In addition, we present a formula for computing the degree
w.r.t the distance variable.Comment: 24 pages, no figure
A note on Chudnovsky's Fuchsian equations
We show that four exceptional Fuchsian equations, each determined by the four
parabolic singularities, known as the Chudnovsky equations, are transformed
into each other by algebraic transformations. We describe equivalence of these
equations and their counterparts on tori. The latter are the Fuchsian equations
on elliptic curves and their equivalence is characterized by transcendental
transformations which are represented explicitly in terms of elliptic and theta
functions.Comment: Final version; LaTeX, 27 pages, 1 table, no figure
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