{
  "abstract": "We prove that the blow-up Z_m of a smooth cubic fourfold along m <= 8 planes, pairwise meeting at distinct points and satisfying explicit generality conditions, is a smooth Fano fourfold of Picard rank rho(Z_m) = m+1 <= 9; in particular, we obtain three new families of smooth Fano fourfolds with rho > 6 that are not a product of surfaces. Complementary to this result, we show that a smooth cubic fourfold as above exists. Moreover, we study the birational geometry of Z_m and show that it corresponds exactly to that of a smooth del Pezzo surfaces S_m, obtained as the blow-up of P^2 along m <= 8 points in general position. Namely, Z_m and S_m have isomorphic Mori cones, pseudo-effective cones with same Mori chamber decomposition, and there is a one-to-one correspondence between the contractions of Z_m and the contractions of S_m. Lastly, we study the anticanonical linear system of Z_m and prove that it is basepoint free if and only if m <= 7. For m = 8 and a special configuration of planes, we show that the anticanonical base locus Bs(|-K_{Z_8}|) has dimension 2 and contains a smooth del Pezzo surface of degree 1.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25532",
  "author_total": 1,
  "authors": [
    {
      "name": "Saverio Andrea Secci"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/84tty60ekj7bd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25532",
  "fulltext_url": null,
  "id": "84tty60ekj7bd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25532",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223008524",
  "pdf_url": "https://arxiv.org/pdf/2610.25532",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/84tty60ekj7bd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25532",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25532"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The blow-up of the cubic fourfold along eight planes is Fano",
  "title_text": "The blow-up of the cubic fourfold along eight planes is Fano",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/84tty60ekj7bd",
  "venue": "arXiv",
  "versions": []
}