Positivity for Higgs Vector Bundles: Criteria and Applications
Abstract Working in the category of smooth projective varieties over an algebraically closed field of characteristic 0, we review notions of ampleness and numerical nefness for Higgs bundles which “feel” the Higgs field and formulate criteria of the Barton-Kleiman type for these notions. We give an application to minimal surfaces of general type that saturate the Miyaoka-Yau inequality, showing that their cotangent bundle is ample.
Authors
- Beatriz Graña Otero (ORCID: https://orcid.org/0000-0003-1666-2685)
- Armando Capasso (ORCID: https://orcid.org/0009-0001-5463-7221)
- Ugo Bruzzo (ORCID: https://orcid.org/0000-0001-8726-1729)
Institutions
- Scuola Internazionale Superiore di Studi Avanzati (IT)
- Universidad de Salamanca (ES)
- Instituto de Física Fundamental (ES)
- Ospedale di Livorno (IT)
- Istituto Nazionale di Fisica Nucleare, Sezione di Trieste (IT)
- Institute for Geometry and Physics
Publication Details
- Journal
- Revista Matemática Complutense
- Published
- 2025-10-28
- DOI
- https://doi.org/10.1007/s13163-025-00551-7
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Scuola Internazionale Superiore di Studi Avanzati
- Universidad de Salamanca
- Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni
- European Regional Development Fund
- Agencia Estatal de Investigación