6 problems

Let $A$ be a domain equipped with an injective well-ordered valuation $\nu$, and let $gr A$ denote the associated graded algebra of the filtration on $A$ induced by $\nu$. A family…

No coalescence conjecture. The coalescence problem does not occur: a one-parameter deformation $f_t$ cannot have more than one instability and satisfy

Contractible stable perturbation conjecture. There are such germs for which

Let $(X,L)$ be a polarized complex variety, and let $\eta\in H^1(X,\mathcal{E}_L)$ be a deformation class of $(X,L)$. A test configuration is compatible with $\eta$ if its first-or…

Constancy conjecture. The graded $\mathbb Z[U]$-module $\mathbb H^*_{an,0}(X_t,o_t)$ is constant along the deformation.

Generic Milnor number sequence conjecture.