5 problems

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Verbitsky's conjecture on exotic hypercomplex structures
A hypercomplex structure $(X,I,J,K)$ is exotic if $(X,I)$ is holomorphically symplectic, but for no choice of $\alpha \in \operatorname{Kahl}(X)$ does the corresponding hyperkähler…
openhypercomplex-geometry hyperkahler-geometry twistor-spaces
03
Uniqueness conjecture for the Moishezon element of the twistor-group action
Moishezon-element uniqueness conjecture. There is a unique Moishezon element in $\Gamma_{\mathcal X}$ , namely the equivalence class of complex conjugation. The conjecture asserts t…
opencomplex-geometry moduli-spaces twistor-spaces
06
Higher-singularity vanishing conjecture for twistor spaces
Let $X \subseteq \operatorname{iGr}(n,2n)$ be the big affine cell, or a ball or a polydisc inside it, and let $Z$ be the corresponding twistor space in the stated double fibration.…
opensheaf-cohomology symplectic-geometry twistor-spaces
05
Local exactness conjecture for singular BGG complexes
The singular BGG complex is constructed on the twistor space $Z'$ associated with a suitably chosen, but arbitrarily small, open subset $X'$ . Local exactness conjecture. The conclu…
openbg-g-complexes sheaf-cohomology twistor-spaces
07
Honda's classification conjecture for Moishezon twistor spaces on $4\bar{\mathbb{CP}}^2$
Honda's classification conjecture. The following assertions should hold:
opencomplex-geometry self-dual-geometry twistor-spaces
03

Verbitsky's conjecture on exotic hypercomplex structures