We show that the linked Grassmannian scheme, which arises in a functorial compactification of spaces of limit linear series, and in local models of certain Shimura varieties, is Cohen-Macaulay, reduced, and flat. We give an application to spaces of limit linear series.

In this paper the flatness [M. Fliess, J. Lévine, P. Martin, and P. Rouchon, Internat. J. Control, 61 (1995), pp. 1327–1361, M. Fliess, J. Lévine, P. Martin, and P. Rouchon, IEEE Trans. Automat. Control, 44 (1999), pp. 922–937] of heavy chain systems, i.e., trolleys carrying a fixed length heavy chain that may carry a load, is addressed in the partial derivatives equations framework. We paramet...

The origin of this report lies in the very interesting discussions with Chal-lamel of the CGES at Ecole des Mines de Paris and with Hugues Mounier of Ecole des Mines de Nantes.

We study the local geometry of irreducible parabolic geometries admitting strongly essential flows; these are flows by local automorphisms with higher-order fixed points. We prove several new rigidity results, and recover some old ones for projective and conformal structures, which show that in many cases the existence of a strongly essential flow implies local flatness of the geometry on an op...

We present two related algorithms for flattening (generating polyline approximations for) curves associated with planar cubic Bézier segments. One flattens the path curve, and the other flattens the left and right offset curves. The algorithm for flattening path curves yields an average of 67% of the vertices generated by recursive subdivision, while maintaining flatness to within 4% of the spe...

We say a graph G is flexibly planar if and only if for every cycle in G, there exists a planar embedding of G such that the cycle bounds a disk whose interior is disjoint from G. We show the complete minor-minimal set of flexibly planar graphs is the single graph K4 We further investigate the property of flexible flatness, a property that has an analogous definition for 3space. We show, with on...