{
  "abstract": "Theorems by Bray-Brendle-Neves and Zhu about positive scalar curvature metrics on products of a 2-sphere and an n-torus suggests that positive scalar curvature suggests and appropriate topological assumptions should lead to the existence of a topologically non trivial 2-spheres of small area, which can be stated as upper bound on the 2-systole of such manifolds. Recent progress have been made in this direction by Sha and Tsiamis under the additional Kähler assumption while Checcini-Hirsh-Ziedler, Stryker and Tsiamis showed similar upper bounds on the stable 2-systole using index theoretic methods. We prove here similar inequalities for some Kähler manifold which control the relative sizes of the representatives of a well chosen set of homology classes. For instance on $(\\mathbb{CP}^1×\\mathbb{CP}^1 , \\omega)$ with a positive scalar curvature Kähler metric we quantitavely show that largeness of one factor imposes smallness of the other one.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.13055",
  "author_total": 2,
  "authors": [
    {
      "name": "Hugues Auvray"
    },
    {
      "name": "Thomas Richard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e8ydnznh4bcyx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.13055",
  "fulltext_url": null,
  "id": "e8ydnznh4bcyx",
  "issns": [],
  "landing_url": "https://u-pec.hal.science/hal-05652259v2",
  "language": "en",
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-dg"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://u-pec.hal.science/hal-05652259/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e8ydnznh4bcyx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:36Z",
      "native_id": "hal-05652259",
      "source": "hal",
      "url": "https://u-pec.hal.science/hal-05652259v2"
    },
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2606.13055",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.13055"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "BALANCING THE 2-SYSTOLES OF SOME KÄHLER MANIFOLDS WITH POSITIVE SCALAR CURVATURE",
  "title_text": "BALANCING THE 2-SYSTOLES OF SOME KÄHLER MANIFOLDS WITH POSITIVE SCALAR CURVATURE",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/e8ydnznh4bcyx",
  "venue": "HAL",
  "versions": []
}