The moduli-deformation conjecture for cubic, $X_{10}$, and Kuechle fourfolds

Consider special four-dimensional cubics, four-dimensional $X_{10}$ varieties, and Kuechle manifolds, together with their Landau–Ginzburg moduli spaces.

Moduli-deformation conjecture. There is an infinite series of associated moduli spaces that can be deformed one to another.

The conjecture extends the proposed deformation picture from cubics and $X_{10}$ varieties to Kuechle manifolds and is part of the source's noncommutative Sarkisov program.