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- Gabriel Taubin, Fernando Cukierman, Steve J Sullivan, Jean Ponce, David J. Kriegman
- IEEE Trans. Pattern Anal. Mach. Intell.
- 1994

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 P… (More)

- Douglas Lanman, Megan Wachs, Gabriel Taubin, Fernando Cukierman
- Third International Symposium on 3D Data…
- 2006

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)

Abstract. Let X ⊂ Pr be a smooth algebraic curve in projective space, over an algebraically closed field of characteristic zero. For each m ∈ N, the m-flexes of X are defined as the points where the osculating hypersurface of degree m has higher contact than expected, and a hypersurface H ⊂ Pr is called a m-Hessian if it cuts X along its m-flexes. When X is… (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)

In this note we analyse the Exceptional Component of the space of integrable forms of degree two, introduced by Cerveau-Lins Neto, in terms of the geometry of Veronese curves and classical invariant theory.

- TANGENT SHEAF, Fernando Cukierman
- 2006

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)

Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a necessary condition for positivity and a sufficient condition for non-negativity, in terms of positivity or… (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)