Skip to content
DraconiticResearch
Search Sources API
186,086 studies31 sourcesUpdated 18 min ago
PreprintarXiv licencearXiv

Non-Archimedean balanced metrics and their application to totally degenerate abelian varieties

  • Keita Goto
Open at sourcePDFDOICite

Abstract

For a polarized complex manifold with discrete automorphism group, it is known that if the first Chern class admits a cscK metric, then the balanced metrics, which are characterized in terms of the algebro-geometric notion of Chow stability, approximate this cscK metric. In this paper, we study a non-Archimedean analogue of this phenomenon. In particular, we prove that such an analogue holds for polarized totally degenerate abelian varieties. As an application, we also show that, for a totally degenerating family of polarized abelian varieties, the validity of this non-Archimedean analogue yields a uniform estimate for the Calabi--Yau metrics on fibers sufficiently close to the degenerate fiber.

Related

  1. Non-archimedean Monge-Ampère measures for toric metrics on subvarieties of toric varieties
    Chenying Lin
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi–Yau hypersurfaces
    Léonard Pille-Schneider
    Algebraic geometryPeer-reviewedCC BYFull text5 citedGeometry & topologyOpenAlex
  3. Good stratifications of non-degenerate locally tame complete intersection varieties
    Kazumasa Inaba
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Inhomogeneous balanced non-Kähler metrics on complex projective spaces
    Brian Grajales, Lino Grama
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  5. A Poincaré-Lefschetz Theorem for Cellular Cosheaves and an Application to the Tropical Homology of Orbifold Toric Varieties
    Jules Chenal
    Annales Henri LebesguePeer-reviewedCC BY 4.0Full textAlgebra & number theoryGeometry & topologyHAL

Cite

BibTeXRIS
BibTeX
@misc{goto2026nonarchimedean,
  title = {{Non-Archimedean balanced metrics and their application to totally degenerate abelian varieties}},
  author = {Keita Goto},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.15758},
  eprint = {2606.15758},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.15758},
}
RIS
TY  - UNPB
TI  - Non-Archimedean balanced metrics and their application to totally degenerate abelian varieties
AU  - Keita Goto
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2606.15758
UR  - https://arxiv.org/abs/2606.15758
AB  - For a polarized complex manifold with discrete automorphism group, it is known that if the first Chern class admits a cscK metric, then the balanced metrics, which are characterized in terms of the algebro-geometric notion of Chow stability, approximate this cscK metric. In this paper, we study a non-Archimedean analogue of this phenomenon. In particular, we prove that such an analogue holds for polarized totally degenerate abelian varieties. As an application, we also show that, for a totally degenerating family of polarized abelian varieties, the validity of this non-Archimedean analogue yields a uniform estimate for the Calabi--Yau metrics on fibers sufficiently close to the degenerate fiber.
ER  -