[2009.12645] $\mathbb Z/2$-Godeaux surfaces Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2009.12645 (math) [Submitted on 26 Sep 2020 ( v1 ), last revised 28 Apr 2026 (this version, v3)] Title: $\mathbb Z/2$-Godeaux surfaces Authors: Eduardo Dias , Carlos Rito View a PDF of the paper titled $\mathbb Z/2$-Godeaux surfaces, by Eduardo Dias and Carlos Rito View PDF HTML (experimental) Abstract: We prove that the moduli space of numerical Godeaux surfaces with torsion group $\mathbb{Z}/2$ is irreducible and unirational of dimension 8. Moreover, we show that the topological fundamental group of these surfaces is also $\mathbb{Z}/2$. Our approach is based on the explicit construction of equations for all universal covers of numerical Godeaux surfaces with torsion group $\mathbb{Z}/2$. Comments: Final version Subjects: Algebraic Geometry (math.AG) MSC classes: 14J29 Cite as: arXiv:2009.12645 [math.AG] (or arXiv:2009.12645v3 [math.AG] for this version) https://doi.org/10.48550/arXiv.2009.12645 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Carlos Rito [ view email ] [v1] Sat, 26 Sep 2020 17:12:34 UTC (158 KB) [v2] Mon, 21 Feb 2022 14:46:37 UTC (158 KB) [v3] Tue, 28 Apr 2026 10:31:18 UTC (248 KB) Full-text links: Access Paper: View a PDF of the paper titled $\mathbb Z/2$-Godeaux surfaces, by Eduardo Dias and Carlos Rito View PDF HTML (experimental) TeX Source view license Ancillary-file links: Ancillary files ( details ) : Case_alpha_1_c_0/1_TheAlgorithm_alpha_1_c_0.txt Case_alpha_1_c_0/2_TheEquations_alpha_1_c_0.txt Case_alpha_1_c_0/3_Verifications_alpha_1_c_0.txt Case_alpha_1_c_0/4_ItIsWeightedProjSpace_alpha_1_c_0.txt Case_alpha_1_c_1/1_TheAlgorithm_alpha_1_c_1.pdf Case_alpha_1_c_1/2_TheEquations_alpha_1_c_1.txt Case_alpha_1_c_1/3_Verifications_alpha_1_c_1.txt Case_alpha_1_c_1/4_ItIsWeightedProjSpace_alpha_1_c_1.txt Case_alpha_2_c_0/TheAlgorithm_alpha_2_c_0.txt Case_alpha_2_c_1/1_TheAlgorithm_alpha_2_c_1.txt Case_alpha_2_c_1/2_TheEquations_alpha_2_c_1.txt Case_alpha_2_c_1/3_Verifications_alpha_2_c_1.txt Case_alpha_2_c_1/4_ItIsWeightedProjSpace_alpha_2_c_1.txt Case_alpha_2_c_1/5_TheOctic_alpha_2_c_1.txt Case_alpha_2_c_1/6_Dimension_alpha_2_c_1.txt Case_alpha_3_c_1/1_TheAlgorithm_alpha_3_c_1.txt Case_alpha_3_c_1/2_TheEquations_alpha_3_c_1.txt Case_alpha_3_c_1/3_Verifications_alpha_3_c_1.txt Case_alpha_3_c_1/4_ItIsWeightedProjSpace_alpha_3_c_1.txt Lemma2.txt Other/Finding_eq_2_for_a2c1.txt Proposition3.txt Theorem4.txt (18 additional files not shown) Current browse context: math.AG < prev | next > new | recent | 2020-09 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from