Huygens' principle is a way to describe the propagation of light rays in a manifold $\mathcal{M}$. Suppose we start with an infinitesimal ball of light at position $X$ in a manifold. Let $B(X,t)$ be the set of points to which light rays can arrive at times less than or equal to $t$. Then $\partial B(X,t)=\Sigma(X,t)$ is a closed surface that constitutes the set of points to which light arrive precisely at time $t$. Consider both $\Sigma(X,t_-)$ and $\Sigma(X,t_+)$

Consider also the class of surfaces $\mathcal{A}(t_--t_+)=\Sigma(Y,t_+-t_-)$ for each $Y\in \Sigma(X,t_-)$

Then $\Sigma(X,t_+)$ is the unique closed surface in $\mathcal{M}$ that is tangent to each element in $\mathcal{A}(t_--t_+)$

This is Huygens' theorem.

My question is whether this can be reframed in the language of algebraic geometry. My question is vague because I know very little in algebraic geometry. I guess I am trying to ask if there is a generalization of Huygens' principle to more exotic spaces like supermanifolds, for instance.

Singularities of differentiable mapsby Arnold, Gusein-Zade and Varchenko, especially section 20.6. $\endgroup$