38 citations · 111 across the 15 of their papers we have counts for
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Varieties of apolar subschemes of toric surfaces
Matteo Gallet, Kristian Ranestad, Nelly Villamizar
Powersum varieties, also called varieties of sums of powers, have provided examples of interesting relations between varieties since their first appearance in the 19th century. One…
Geometrically continuous splines for surfaces of arbitrary topology
Bernard Mourrain, Raimundas Vidunas, Nelly Villamizar
We analyze the space of geometrically continuous piecewise polynomial functions or splines for quadrangular and triangular patches with arbitrary topology and general rational tran…
Bounds on the dimension of trivariate spline spaces: A homological approach
Bernard Mourrain, Nelly Villamizar
We consider the vector space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain partitioned into tetrahedra. We prove new lo…
Degenerations of real irrational toric varieties
Elisa Postinghel, Frank Sottile, Nelly Villamizar
An irrational toric variety X is an analytic subset of the simplex associated to a finite configuration of real vectors. The positive torus acts on X by translation, and we conside…
Homological techniques for the analysis of the dimension of triangular spline spaces
Bernard Mourrain, Nelly Villamizar
The spline space attached to a subdivided domain of is the vector space of functions of class which are polynomials of degree on each piece…