Coincidence of geometric and algebraic deformations

Determine whether geometric deformations and algebraic flat deformations of contraction algebras coincide in general.

Background

The paper concerns flat deformations of contraction algebras to semisimple algebras whose matrix-block multiplicities are predicted by geometry and Gopakumar–Vafa invariants. Although geometric and algebraic deformation theories produce related constructions, the general relationship between them is unresolved. The results establish such deformations for the first class of type E contraction algebras, but do not settle whether the two notions coincide for arbitrary contraction algebras.

References

However, in general it is not known if geometric and algebraic deformations coincide.

— On computing deformations of contraction algebras of type E  (2610.10157 - Smoktunowicz et al., 7 Oct 2026) in Section 1, Introduction

These questions were answered in the affirmative for contraction algebras of types $A$ and $D$ , however the case of contraction algebras of type $E$ remained open.

— On computing deformations of contraction algebras of type E  (2610.10157 - Smoktunowicz et al., 7 Oct 2026) in Section 1, Introduction