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Latin trades can be interpreted geometrically as oriented surfaces. Those of genus zero are called spherical. The paper contains a construction that shows how all latin trades can be obtained from the spherical ones by a cut-and-paste method that raises the genus
We study configurations of 2-planes in that are combinatorially described by the Petersen graph. We discuss conditions for configurations to be locally Cohen–Macaulay and describe the Hilbert scheme of such arrangements. An analysis of the homogeneous ideals of these configurations leads, via...
We adapt numerical continuation methods to compute all solutions of finite difference discretizations of nonlinear boundary value problems involving the Laplacian in two dimensions. New solutions on finer meshes are obtained from solutions on coarser meshes using a complex homotopy deformation....
Unstable minimal surfaces are the unstable stationary points of the Dirichlet integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used, an application of which was presented in Struwe, J. Reine Angew. Math. 349: 1–23,...
Izmestiev and Joswig described how to obtain a simplicial covering space (the partial unfolding ) of a given simplicial complex, thus obtaining a simplicial branched cover Adv. Geom. 3:191–255, 2003. We present a large class of branched covers which can be constructed via the partial unfolding....
Let X ⊂ be a smooth variety. The embedding in gives naturally rise to the notion of embedded tangent spaces. That is the locus spanned by tangent lines to a point x ∈ X . Generally the embedded tangent space intersects the variety X only at the point x . In this paper I am interested in those X...
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