Smooth Calabi-Yau varieties with large index and Betti numbers

[2502.07031] Smooth Calabi-Yau varieties with large index and Betti numbers Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2502.07031 (math) [Submitted on 10 Feb 2025 ( v1 ), last revised 30 Jan 2026 (this version, v2)] Title: Smooth Calabi-Yau varieties with large index and Betti numbers Authors: Jas Singh View a PDF of the paper titled Smooth Calabi-Yau varieties with large index and Betti numbers, by Jas Singh View PDF HTML (experimental) Abstract: A normal variety $X$ is called Calabi-Yau if $K_X \sim_{\mathbb Q} 0$. The index of $X$ is the smallest positive integer $m$ so that $m K_X \sim 0$. We construct smooth, projective Calabi-Yau varieties in every dimension with doubly exponentially growing index, which we conjecture to be maximal in every dimension. We also construct smooth, projective Calabi-Yau varieties with extreme topological invariants; namely, their Euler characteristics and the sums of their Betti numbers grow doubly exponentially. These are conjecturally extremal in every dimension. The varieties we construct are known in small dimensions but we believe them to be new in general. This work builds off of the singular Calabi-Yau varieties found by Esser, Totaro, and Wang in arXiv:2209.04597 . Comments: 32 pages, 10 figures, updated with corrections on well-formedness and star-shapedness Subjects: Algebraic Geometry (math.AG) MSC classes: 14J32 (Primary) 14E30, 14M25, 14J40 (Secondary) Cite as: arXiv:2502.07031 [math.AG] (or arXiv:2502.07031v2 [math.AG] for this version) https://doi.org/10.48550/arXiv.2502.07031 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Mathematische Zeitschrift, Volume 312, article number 105, (2026) Related DOI : https://doi.org/10.1007/s00209-026-03984-y Focus to learn more DOI(s) linking to related resources Submission history From: Jas Singh [ view email ] [v1] Mon, 10 Feb 2025 20:51:47 UTC (30 KB) [v2] Fri, 30 Jan 2026 19:20:20 UTC (33 KB) Full-text links: Access Paper: View a PDF of the paper titled Smooth Calabi-Yau varieties with large index and Betti numbers, by Jas Singh View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2025-02 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

Related documents

• Near horizon limit of the Wang--Yau quasi-local mass#652013
• Near horizon limit of the Wang--Yau quasi-local mass#650560
• A Counterexample to the Huneke-Wiegand Conjecture#984525
• Fixed-locus relations and purely non-symplectic automorphisms of order 6 on K3 surfaces#1014452
• Integral Bott--Chern cohomology of Generalized Calabi--Eckmann threefolds#1130279