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math.AG2023
Questions about the dynamics on a natural family of affine cubic surfaces
Julio Rebelo, Roland Roeder
We present several questions about the dynamics of the group of holomorphic automorphisms of the affine cubic surfaces $$S_{A,B,C,D} = \{(x,y,z) \in \mathbb{C}^3 \, : \, x^2 + y^2…
math.DS2023
Examples of Harmonic Foliated Currents and Singular Levi-flats on the Projective Plane
Mohamad Alkateeb, Julio Rebelo
We provide examples of foliations on the complex projective plane $\CP^2$ carrying positive foliated harmonic currents whose supports coincide with singular Levi-flats which, in tu…
math.DS2023
Global dynamics and perspectives on singularities of holomorphic foliations
Julio C. Rebelo, Helena Reis
In dimensions greater than or equal to 3, the local structure of a singular holomorphic foliation conceals a globally defined foliation on the projective space of dimension one les…