Fukasawa, Satoru Examples of plane curves admitting the same Galois closure for two projections. (English) Zbl 1495.14040 Commun. Algebra 50, No. 10, 4188-4190 (2022). Let \(C\subset \mathbb{P}^{2}\) be an irreducible plane curve of degree \(d\geqslant 4\) over an algebraically closed field \(k\) of characteristic \(p\geqslant 0\), and for a point \(P\in\mathbb{P}^{2}\), let \(L_{P}\) be the Galois closure of \(k(C)/\pi^{\ast}_{P}(\mathbb{P}^{1})\), where \(k(C)\) is the function field of \(C\), and \(\pi_{P}: C \dashrightarrow \mathbb{P}^{1}\) is the projection from \(P\).Based on the work [S. Fukasawa et al., “Algebraic curves admitting the same Galois closure for two projections”, Ann. Mat. Pura Appl (2022; doi:10.1007/s10231-022-01191-0)], and considering the characteristic different from \(2\), in this article the author provides new examples of plane curves in which the Galois closures \(L_{P_{1}}\) and \(L_{P_{2}}\) of projections from two points \(P_{1}\) and \(P_{2}\) are the same. Reviewer: Mariana Coutinho (São Carlos) MSC: 14H05 Algebraic functions and function fields in algebraic geometry 14H37 Automorphisms of curves 14H50 Plane and space curves Keywords:automorphism group; Galois closure; Galois group; plane curve; uniform projection PDFBibTeX XMLCite \textit{S. Fukasawa}, Commun. Algebra 50, No. 10, 4188--4190 (2022; Zbl 1495.14040) Full Text: DOI References: [1] Cifani, M. G.; Cuzzucoli, A.; Moschetti, R., Monodromy of projections of hypersurfaces, Ann. Mat. Pura Appl, 201, 637-654 (2022) · Zbl 1485.14050 [2] Fukasawa, S., A birational embedding of an algebraic curve into a projective plane with two Galois points, J. Algebra, 511, 95-101 (2018) · Zbl 1400.14084 [3] Fukasawa, S.; Higashine, K.; Takahashi, T., Algebraic curves admitting the same Galois closure for two projections, Ann. Mat. Pura Appl (2022) · Zbl 1504.14052 · doi:10.1007/s10231-022-01191-0 [4] Pirola, G. P.; Schlesinger, E., Monodromy of projective curves, J. Algebraic Geom, 14, 623-642 (2005) · Zbl 1084.14011 [5] Yoshihara, H., Function field theory of plane curves by dual curves, J. Algebra, 239, 340-355 (2001) · Zbl 1064.14023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.