Conceptual explanation of the Gale-duality correspondence for logarithmic vector fields

Determine whether the correspondence under Gale duality between the logarithmic vector fields ψ_{i→k} of D_{3,5} and the corresponding fields ψ'_{k→i} of D_{2,5} admits a conceptual explanation at the level of logarithmic vector fields.

Background

The paper observes that Gale duality sends the Pluecker coefficients defining the degree-ten logarithmic vector fields for D_{3,5} to the coefficients of analogous logarithmic fields for D_{2,5}. Although the correspondence is explicit at the level of formulas, the fields behave differently with respect to minimal generation: the D_{2,5} fields are logarithmic but are not minimal generators, whereas the corresponding D_{3,5} fields contribute minimal generators.

The author explicitly leaves open whether this algebraic relationship reflects a deeper conceptual mechanism in the theory of logarithmic derivations and Gale duality.