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We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.
For a homogeneous linear differential equation defined over a differential field K, a Picard-Vessiot extension is a differential field extension of K differentially generated by a fundamental system of solutions of the equation and not adding constants. When K has characteristic 0 and the field...
We state and consider the Gabrielov–Khovanskii problem of estimating the multiplicity of a common zero for a tuple of polynomials in a subvariety of a given codimension in the space of tuples of polynomials. For a bounded codimension we obtain estimates of the multiplicity of the common zero,...
We propose a generalization of the classical notions of plumbing and Murasugi summing operations to smooth manifolds of arbitrary dimensions, so that in this general context Gabai’s credo “the Murasugi sum is a natural geometric operation” holds. In particular, we prove that the sum of the pages...
The geometry of Kepler’s problem is elucidated by lifting the motion from the (x, y)-plane to the cone
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