85 citations · 91 across the 6 of their papers we have counts for
7 papers
Enumerative geometry of Legendrian foliations: a Tale of Contact
Mauricio Corrêa, Israel Vainsencher
A contact distribution on projective three-space is defined by the 1-form , up to a change of projective coordinates. The family of contact distrib…
Linear Pullback components of the space of codimension one foliations
V. Ferrer, I. Vainsencher
The space of holomorphic foliations of codimension one and degree in () has an irreducible component whose general element can be written as a pul…
Degree of the exceptional component of foliations in P3
Artur Rossini, Israel Vainsencher
The purpose of this work is to obtain the degree of the exceptional component of the space of holomorphic foliations of degree two and codimension one in P^3. We construct a parame…
Enumeration of surfaces containing an elliptic quartic curve
Fernando Cukierman, Angelo Lopez, Israel Vainsencher
A very general surface of degree at least four in projective space of dimension three contains no curves other than intersections with surfaces. We find a formula for the degree of…
Polynomial vector fields with algebraic trajectories
Viviana Ferrer, Israel Vainsencher
It is known after Jouanolou that a general holomorphic foliation of degree in projective space has no algebraic leaf. We give formulas for the degrees of the subvarieties o…
Flatness of families induced by hypersurfaces on flag varieties
Israel Vainsencher
We answer a question posed by S. Kleiman concerning flatness of the family of complete quadrics. We also show that any flat family of hypersurfaces on Grassmann varieties induces a…
Enumeration of -fold tangent hyperplanes to a surface
Israel Vainsencher
For each we present formulas for the number of nodal curves in an dimensional linear system on a smooth, projective surface. This yields in particular the nu…