{
  "abstract": "Using determinantal divisors of integral matrices, that is, greatest common divisors of minors of fixed order, we introduce the notion of type of a homomorphism $f$ of complex tori, which is similar to the type of a polarization. We show that the type is invariant under composition with isomorphisms, and that it completely describes the kernel of $f$ as a group. More precisely, the quotient of the kernel by its connected component containing 0 is a product of cyclic groups whose orders are determined by the type of $f$. Since the type can be computed from any rational representation of $f$, this gives an effective way to determine the kernel of a homomorphism. As a consequence, we compute the classic invariants degree and exponent of $f$, when $f$ has finite kernel. When $f$ is an isogeny, we also compute the type of its inverse isogeny from that of $f$. Finally, we compare the type of a polarization to the type of its associated isogeny.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28655",
  "author_total": 1,
  "authors": [
    {
      "name": "Juliana Coelho"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1t73j10433cj6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28655",
  "fulltext_url": null,
  "id": "1t73j10433cj6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28655",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204893579",
  "pdf_url": "https://arxiv.org/pdf/2608.28655",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1t73j10433cj6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.28655",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28655"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Type of homomorphisms of complex tori",
  "title_text": "Type of homomorphisms of complex tori",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/1t73j10433cj6",
  "venue": "arXiv",
  "versions": []
}