7 citations · 21 across the 18 of their papers we have counts for
21 papers
Confocal families of plane algebraic curves
Ragni Piene, Boris Shapiro
We study families of plane algebraic curves sharing the same set of foci. We reformulate confocality via a focal map on equiclassical families and analyze its fibers using deformat…
Envelopes and evolutes
Ragni Piene
The study of evolutes of plane curves goes back at least to Huygens, and was continued and extended to space curves by Monge, Darboux, and others. Salmon studied projective curves…
On fundamental forms and osculating bundles
Raquel Mallavibarrena, Ragni Piene
We define higher order fundamental forms and osculating spaces of projective algebraic varieties, using sheaves of principal parts. We show that the th fundamental form can be v…
Interpolation of toric varieties
Alicia Dickenstein, Sandra Di Rocco, Ragni Piene
Let be a -dimensional variety in -dimensional projective space. Let be a positive integer such that . Consider the following in…
Node Polynomials for Curves on Surfaces
Steven Kleiman, Ragni Piene
We complete the proof of a theorem we announced and partly proved in [Math. Nachr. 271 (2004), 69-90, math.AG/0111299]. The theorem concerns a family of curves on a family of surfa…
Return of the plane evolute
Ragni Piene, Cordian Riener, Boris Shapiro
Below we consider the evolutes of plane real-algebraic curves and discuss some of their complex and real-algebraic properties. In particular, for a given degree , we provid…