\(\operatorname{Spin}(7)\)-instantons, stable bundles and the Bogomolov inequality for complex 4-tori

DOI10.1016/j.matpur.2013.11.004zbMath1326.14107arXiv1302.2846OpenAlexW2093181666MaRDI QIDQ2453266

Vicente Muñoz

Publication date: 6 June 2014

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.2846

zbMATH Keywords

abelian varietyperiod matricesBogomolov inequalitystable bundle\(\operatorname{Spin}(7)\)-instanton

Mathematics Subject Classification ID

Period matrices, variation of Hodge structure; degenerations (32G20) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Spin and Spin({}^c) geometry (53C27) Complex multiplication and abelian varieties (14K22) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21) (G)-structures (53C10)

Related Items (6)

Mirror of volume functionals on manifolds with special holonomy ⋮ Fourfolds of Weil type and the spinor map ⋮ The monodromy of generalized Kummer varieties and algebraic cycles on their intermediate Jacobians ⋮ Transversality for the moduli space of Spin(7)-instantons ⋮ On rotation of complex structures ⋮ Deformations of nearly Kähler instantons

Cites Work

• Stable bundles on hypercomplex surfaces
• A generalization of the notion of instanton
• Stable bundles with small \(c_2\) over 2-dimensional complex tori
• Hodge classes on abelian varieties of low dimension
• Gauge theory and calibrated geometry. I
• Stable vector bundles as generators of the Chow ring
• A note of Shimura's paper: Discontinuous groups and Abelian varieties
• Spin(7) instantons and the Hodge Conjecture for certain abelian four-folds: a modest proposal
• A Survey of the Hodge Conjecture
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