5 problems

Decomposition Conjecture. Every compact Fujiki manifold with vanishing first Chern class admits such a finite étale cover and decomposition, together with the stated bimeromorphic…

Let $X$ be a compact Kähler manifold with nef anticanonical class. Denote its universal cover by $\widetilde{X}$. Decomposition conjecture. The universal cover decomposes as a prod…

Primitive symplectic decomposition conjecture. Primitive symplectic varieties should be building blocks in a singular version of the Beauville–Bogomolov decomposition theorem. This…

Updated decomposition conjecture. Every near-regular matroid can be obtained from signed-graphic matroids, the duals of signed-graphic matroids, or members of a finite set…

Whittle's decomposition conjecture. Every near-regular matroid can be obtained from signed-graphic matroids, their duals, and members of some finite set by applying $1$-, $2$-, and…