The theory of integrability plays an important role in the study of the dynamics of differential
systems. This theory is related to several branches of mathematics, such as algebraic …

We solve the Poincaré problem for plane foliations with only one dicritical divisor. Moreover,
in this case, we give a simple algorithm that decides whether a foliation has a rational first …

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 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 …

We provide an algorithm which decides whether a polynomial foliation $\mathcal
{F}^{\mathbb {C}^ 2} $ on the complex plane has a polynomial first integral of genus $ g\neq …

We present a survey of some aspects and new results on configurations, ie disjoint unions of
constellations of infinitely near points, local and global theory, with some applications and …

We give an algorithm for deciding whether a planar polynomial differential system has a first
integral which factorizes as a product of defining polynomials of curves with only one place …

We give a characterization theorem for non-degenerate plane foliations of degree different
from 1 having a rational first integral. Moreover, we prove that the degree $ r $ of a non …

Lins Neto's examples of foliations and the Mori cone of blowâ•’ups of â—Ž²
Page 1 Bull. London Math. Soc. 43 (2011) 335–346 Cо2011 London Mathematical Society …