Abstract
Minimal algebraic surfaces of general type X such that \(K^2_X=2\chi ({\mathcal {O}}_X)-6\) or \(K^2_X=2\chi ({\mathcal {O}}_X)-5\) are called Horikawa surfaces. In this note we study \({\mathbb {Z}}^2_2\)-actions on Horikawa surfaces. The main result is that all the connected components of Gieseker’s moduli space of canonical models of surfaces of general type with invariants satisfying these relations contain surfaces with \({\mathbb {Z}}^2_2\)-actions.
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The author is deeply indebted to his supervisor Margarida Mendes Lopes for all her help. The author also thanks the anonymous reviewer for her/his thorough reading of the paper and suggestions.
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The author is a doctoral student of the Department of Mathematics and Center for Mathematical Analysis, Geometry and Dynamical Systems of Instituto Superior Técnico, Universidade de Lisboa and is supported by Fundacāo para a Ciência e a Tecnologia (FCT), Portugal through the program Lisbon Mathematics Ph.d. (LisMath), scholarship FCT-PD/BD/128421/2017 and Projects UID/MAT/04459/2019 and UIDB/04459/2020.
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Lorenzo, V. \({\mathbb {Z}}_2^2\)-actions on Horikawa surfaces. manuscripta math. 168, 535–547 (2022). https://doi.org/10.1007/s00229-021-01303-9
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DOI: https://doi.org/10.1007/s00229-021-01303-9