{"id":"palomar/PALOMAR-2026-09-18-000007","url":"https://github.com/carlok/sharp-symmetry-bounds-lean/tree/ced9fe2d4d2aa42aa03bbc19b1b56cdcd18c9413","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-18-000007-v1.json","repo":"https://github.com/carlok/sharp-symmetry-bounds-lean","tags":["math.AG","math.MG","msc:14H50","msc:14P05","msc:51N20","algebraic-geometry","symmetry","plane-curves"],"score":0,"title":"Sharp symmetry bounds for real plane algebraic curves (Theorem 1)","trust":"high","domain":"math.AG","source":"palomar","authors":["Carlo Perassi"],"reviews":0,"subject":"math.AG","summary":"Let C be an infinite real plane algebraic curve defined by a polynomial of degree d >= 2 that is irreducible over the complex numbers, and suppose C is not a circle. Its group of Euclidean symmetries is finite, the orientation-preserving part is cyclic of order at most max(d, 2d - 4), and the full group has order at most 2d. Both bounds are attained in every degree d >= 2. For d >= 5, curves attaining the rotation bound are exactly, up to orientation-preserving similarity, the curves Re(z^(d-2)(|z|^2 + a)) = 0 with |a| = 1 and a not real; conversely each such curve with d - 2 >= 3 attains…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-18","reactions":{},"formalized":true,"formalizes":[{"title":"Sharp symmetry bounds for real algebraic curves (working draft, 2026), Theorem 1","identifier":"","relationship":"formalizes"}]}