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Families of singular algebraic varieties that are rationally elliptic spaces

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  • A. Libgober

Abstract

We discuss families of hypersurfaces with isolated singularities in projective space with the property that the sum of the ranks of the rational homotopy and the homology groups is finite. They represent infinitely many distinct homotopy types with all hypersurfaces having a nef canonical or anti‐canonical class. In the Appendix, we show that such an infinite family of smooth rationally elliptic 3‐folds does not exist.

Suggested Citation

  • A. Libgober, 2026. "Families of singular algebraic varieties that are rationally elliptic spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 299(1), pages 214-223, January.
    • Handle: RePEc:bla:mathna:v:299:y:2026:i:1:p:214-223
    DOI: 10.1002/mana.70092
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