Abstract
The automorphism group of a curve is studied from the viewpoint of the canonical embedding and Petri’s theorem. A criterion for identifying the automorphism group as an algebraic subgroup the general linear group is given. Furthermore, the action of the automorphism group is extended to a linear action on the generators of the minimal free resolution of the canonical ring of the curve X.
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Acknowledgements
The authors would like to thank H. Charalambous and K. Karagiannis for useful discussions concerning this article and their suggestions and corrections. The first author would like to also thank G. Cornelissen for introducing him to Petri’s theorem. We would like also to thank the anonymous referee for her/his comments and remarks. The second author received partial financial support from the Mathematics Department of the University of Athens and from the Tsakyrakis scholarship. The third author is co-financed by Greece and the European Union (European Social Fund—ESF) through the Operational Programme “Human Resources Development, Education and Lifelong Learning” in the context of the project “Strengthening Human Resources Research Potential via Doctorate Research” (MIS-5000432), implemented by the State Scholarships Foundation (IKY) (12133).
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Kontogeorgis, A., Terezakis, A. & Tsouknidas, I. Automorphisms and the Canonical Ideal. Mediterr. J. Math. 18, 261 (2021). https://doi.org/10.1007/s00009-021-01878-3
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DOI: https://doi.org/10.1007/s00009-021-01878-3