7 problems

Graded-root determination conjecture. The graded root $\big(R(C,o),\chi\big)$ is determined by the lattice cohomology module $\mathbb{H}^0(C,o)$.

Let $\{(C_t,o)\}_{t\in(\mathbb C,0)}$ be a flat deformation of isolated curve singularities. For each level $n$, let $\ell^*$ denote a vertex of the level set of the generic fibre…

Let $(C_t,o)$ be a $\delta$-constant flat deformation of Gorenstein curves. The associated graded graph map … is the map constructed from the deformation, and the graded roots carry…

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

Analytic lattice cohomology conjecture. The morphism

Derived-groups conjecture. The groups $A'$ and $A”$ are isomorphic, up to a grading shift, to the groups $B'$ and $B”$, respectively.

Let $L=S^3_{-d}(K)$ be the link of a superisolated surface singularity corresponding to a rational cuspidal projective plane curve of degree $d$. Let…