Generic symmetry defect set of an algebraic curve

Dias, L.; Farnik, M.; Jelonek, Z.

doi:10.1090/proc/16741

Generic symmetry defect set of an algebraic curve
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by L. R. G. Dias, M. Farnik and Z. Jelonek;

Proc. Amer. Math. Soc. 152 (2024), 2739-2749

DOI: https://doi.org/10.1090/proc/16741

Published electronically: May 7, 2024

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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 as well as degree, genus and Euler characteristic for $X_d$ being a generic (smooth and transversal to the line at infinity) curve of degree $d$ in $\mathbb {C}^2$.

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