A non-algebraizable foliation
It is presented an example of a holomorphic foliation of a non-algebraizable surface which is topologically equivalent to an algebraic foliation.
math.CV↗
arXiv subjects
Paulo Sad
Publications and source records attributed to Paulo Sad.
Non-algebraizable neighborhoods of curves
We provide several families of compact complex curves embedded in smooth complex surfaces such that no neighborhood of the curve can be embedded in an algebraic surface. Different constructions are proposed, by patching neighborhoods of curves in projective surfaces, and blowing down exceptional curves. These constructions generalize examples recently given by S. Lvovski. One of our non algebraic argument is based on an extension theorem of S. Ivashkovich.
math.AG↗
Example of a foliation for Ueda type one
We give an example of a regular 2-dimensional foliation along a curve of genus 3 whose Ueda type is one and normal bundle is of order two
math.AG↗
Regular Foliations and Trace Divisors
An example is given of a divisor of a curve which is not a trace divisor of a foliation.
math.DS↗
Extension of germs of holomorphic foliations
We consider the problem of extending germs of plane holomorphic foliations to foliations of compact surfaces. We show that the germs that become regular after a single blow up and admit meromorphic first integrals can be extended, after local changes of coordinates, to foliations of compact surfaces. We also show that the simplest elements in this class can be defined by polynomial equations. On the other hand we prove that, in the absence of meromorphic first integrals there are uncountably many elements without polynomial representations.
math.CV↗
Embedded Curves and Foliations
We prove the existence of regular foliations with a prescribed tangency divisor in neighborhoods of negatively embedded holomorphic curves; this is related to a linearization theorem due to Grauert. We give also examples of neighborhoods which can not be linearized.
math.CV↗