Generic symmetry defect set of an algebraic curve

Abstract

Let X ⊂ C 2 n X \subset \mathbb {C}^{2n} be an n n -dimensional algebraic variety. We define the algebraic version of the generic symmetry defect set (Wigner caustic) of X X . Moreover, we compute its singularities as well as degree, genus and Euler characteristic for X d X_d being a generic (smooth and transversal to the line at infinity) curve of degree d d in C 2 \mathbb {C}^2 .