In this paper we provide sufficient conditions for maps of vector bundles on smooth
projective varieties to be uniquely determined by their degeneracy schemes. We then …

We prove that a foliation on CP^ 2 CP 2 of degree d with a singular point of type saddle-
node with Milnor number d^ 2+ d+ 1 d 2+ d+ 1 does not have invariant algebraic curves. We …

Foliations in the complex projective plane are uniquely determined by their singular locus,
which is in correspondence with a zero-dimensional ideal. However, this correspondence is …

Let X be a smooth projective variety. We show that the map that sends a codimension one
distribution on X to its singular scheme is a morphism from the moduli space of distributions …

In this work, we begin by showing that a holomorphic foliation with singularities is reduced if
and only if its normal sheaf is torsion-free. In addition, when the codimension of the singular …

We study foliations ℱ on Hirzebruch surfaces S δ and prove that, similarly to those on the
projective plane, any ℱ can be represented by a bi-homogeneous polynomial affine 1-form …

We study the class of planar polynomial vector fields admitting Darboux first integrals of the
type∏ i= 1 rfi α i, where the α i's are positive real numbers and the fi's are polynomials …

We propose a linear version of the weighted bounded negativity conjecture. It considers a
smooth projective surface $ X $ over an algebraically closed field of characteristic zero and …

We study algebraic integrability of complex planar polynomial vector fields X= A (x, y)(∂/∂
x)+ B (x, y)(∂/∂ y) through extensions to Hirzebruch surfaces. Using these extensions, each …

Mathematical Research Letters 10, 651–658 (2003) ON SECTIONS WITH ISOLATED
SINGULARITIES OF TWISTED BUNDLES AND APPLICATIONS T Page 1 Mathematical …