Fernando Cukierman

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This paper demonstrates that, for axial non-central optical systems, the equation of a 3D line can be estimated using only four points extracted from a single image of the line. This result, which is a direct consequence of the lack of vantage point, follows from a classic result in enumerative geometry: there are exactly two lines in 3-space which(More)
Let S ⊂ P be a smooth variety over an algebraically closed field of characteristic 0. Denote by D ⊂ P̌ the dual variety of S, consisting of all the hyperplanes in P that are tangent to S. The basic question that we consider in this note is: if X ∈ D is a singular hyperplane section of S, what is the multiplicity mXD of D at X? Our answer is in the style of(More)
We show that the set of singular holomorphic foliations on projective spaces with split tangent sheaf and good singular set is open in the space of holomorphic foliations. We also give a cohomological criterion for the rigidity of holomorphic foliations induced by group actions and prove the existence of rigid codimension one foliations of degree n− 1 on Pn(More)
We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space Fq(r, d) of singular foliations of codimension q and degree d on the complex projective space P , when 1 ≤ q ≤ r − 2. We study the geometry of these irreducible components. In particular we prove that they are all(More)