2023/03/02 by Giulio Bresciani, Bresciani, Giulio
Mathematics · Arts and Humanities · #Algebraic Geometry and Number Theory #Historical Studies and Socio-cultural Analysis #French Historical and Cultural Studies
paper · pdf · doi:10.48550/arxiv.2303.01454
We prove that a smooth, complex plane curve of odd degree can be defined by a polynomial with coefficients in ℝ if and only if it is isomorphic to its complex conjugate; there are counterexamples in even degree. Over arbitrary base fields of characteristic 0, we prove that a smooth plane curve of degree prime with 6 can be defined by a polynomial with coefficients in the field of moduli. We also prove results about fields of moduli of algebraic cycles in ℙ2. In particular, these apply to singular plane curves of arbitrary degree, too.