























This paper has been withdrawn by Giulio Bresciani
No PDF available, click to view other formats
Abstract:We prove that a smooth, complex plane curve $C$ of odd degree can be defined by a polynomial with real coefficients if and only if $C$ is isomorphic to its complex conjugate. Counterexamples are known for curves of even degree.
More generally, we prove that a plane curve $C$ over an algebraically closed field $K$ of characteristic $0$ with field of moduli $k_{C}\subset K$ is defined by a polynomial with coefficients in $k'$, where $k'/k_{C}$ is an extension with $[k':k_{C}]\le 3$ and $[k':k_{C}]\mid \operatorname{deg} C$.
From: Giulio Bresciani [view email]
[v1]
Thu, 21 Sep 2023 15:58:53 UTC (14 KB)
[v2]
Wed, 17 Jun 2026 09:38:28 UTC (1 KB) (withdrawn)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。