2 problems

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The core-map decomposition conjecture
Core-map decomposition conjecture. For any such $X$ ,
Conjectureopenfibrations kahler-manifolds specialnessarXiv posted 2 days ago
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The Kähler h-principle specialness conjecture
Kähler h-principle specialness conjecture. Every compact Kähler manifold satisfying the $h$ -principle should be special.
Conjectureopenh-principle kahler-manifolds specialnessarXiv posted 2 days ago

The core-map decomposition conjecture