Prime Fano $4$-folds with semi-free torus actions

Nicholas Lindsay

Prime Fano $4$-folds with semi-free torus actions

Algebraic Geometry 2026-02-13 v3

Authors: Nicholas Lindsay

Abstract

Let $X$ be a smooth complex prime Fano fourfold having a semi-free action of $\mathbb{C}^*$ , then $X$ is contained in one of the families $\mathbb{P}^4,Q^4,W_5, X^{m}_{8}$ . All of the families contain members that have a semi-free $\mathbb{C}^*$ -action.

Keywords

Fano fourfold semi-free action torus action prime Fano varieties projective geometry

Cite

@article{arxiv.2510.17230,
  title  = {Prime Fano $4$-folds with semi-free torus actions},
  author = {Nicholas Lindsay},
  journal= {arXiv preprint arXiv:2510.17230},
  year   = {2026}
}

Comments

44 pages. In the symplectic result Theorem C the assumption that M is simply connected is needed. Since smooth Fano varieties are simply connected, the proof of the algebraic results Theorem A and Theorem B are not affected. In addition, some misprints are corrected and minor expositional changes are made

Prime Fano $4$-folds with semi-free torus actions

Abstract

Keywords

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