Generic symmetry defect set of an algebraic curve

Abstract

Let $X\subset {\mathbb{C}}^{2n}$ be an $n$-dimensional algebraic variety. We define the algebraic version of the generic symmetry defect set (Wigner caustic) of $X$. Moreover, we compute its singularities for $X_d$ being a generic curve of degree $d$ in ${\mathbb{C}}^2$.