7 problems

Exactness of the transport sequence for non-simple surfaces
arXiv@arxiv
Let the sequence referred to as … should still be exact in the non-simple cases. The conjecture concerns a result beyond the reach of the current proof; exactness is also not recov…
Conjectureopendifferential-geometry twistor-spaces
0
Verbitsky's conjecture on exotic hypercomplex structures
arXiv@arxiv
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…
Conjectureopenhypercomplex-geometry hyperkahler-geometry twistor-spaces
0
Uniqueness conjecture for the Moishezon element of the twistor-group action
arXiv@arxiv
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…
Conjecturesolvedcomplex-geometry moduli-spaces twistor-spaces
0
Higher-singularity vanishing conjecture for twistor spaces
arXiv@arxiv
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.…
Conjectureopensheaf-cohomology symplectic-geometry twistor-spaces
0
Local exactness conjecture for singular BGG complexes
arXiv@arxiv
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…
Conjectureopenbg-g-complexes sheaf-cohomology twistor-spaces
0
Honda's classification conjecture for Moishezon twistor spaces on $4\bar{\mathbb{CP}}^2$
arXiv@arxiv
Honda's classification conjecture. The following assertions should hold:
Conjectureopencomplex-geometry self-dual-geometry twistor-spaces
0
LeBrun's conjecture on Fano contact manifolds
arXiv@arxiv
A Fano contact manifold is a Fano complex contact manifold, and a twistor space of a quaternionic-Kähler manifold is the twistor space associated with a quaternionic-Kähler manifol…
Conjectureopencontact-geometry quaternionic-kahler-geometry twistor-spaces
1

7 problems

Exactness of the transport sequence for non-simple surfaces

Verbitsky's conjecture on exotic hypercomplex structures

Uniqueness conjecture for the Moishezon element of the twistor-group action

Higher-singularity vanishing conjecture for twistor spaces

Local exactness conjecture for singular BGG complexes

Honda's classification conjecture for Moishezon twistor spaces on 4CPˉ24\bar{\mathbb{CP}}^24CPˉ2

LeBrun's conjecture on Fano contact manifolds

Honda's classification conjecture for Moishezon twistor spaces on $4\bar{\mathbb{CP}}^2$