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Complex $2$ manifold $M$ with a given real 2 dimensional submanifold which meets all complex limit cycles of foliations of $M$

MathOverflow Asked by Ali Taghavi on December 17, 2020

Is there a $2$ dimensional holomorphic manifold $M$ with a closed $2$ dimensional real submanifold $A$ of $M$ such that for every singular holomorphic foliation of $M$, all leaf with non trivial holonomy must necessarilly intersect $A$.

Two motivations for this questions are:

1)The minimal set problem in the theory of $SHF$C of $mathbb{C}P^2$

2)This $RG$ preprint "A complex Limit cycle Not Intersecting of the real plane"

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