2013/06/24 by Yuuji Tanaka, Tanaka, Yuuji
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1306.5590
openalex publication_date 2013/06/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider a version of Hermitian-Einstein equation but perturbed by a Higgs field with a solution called a Donaldson-Thomas instanton on compact Kähler threefolds. The equation could be thought of as a generalization of the Hitchin equation on Riemann surfaces to Kähler threefolds. In the appendix of arXiv:0805.2192, following an analogy with the Hitchin equation, we introduced a stability condition for a pair consisting of a locally-free sheaf over a compact Kähler threefold and a section of the associated sheaf of the endomorphisms tensored by the canonical bundle of the threefold. In this article, we prove a Hitchin--Kobayashi-type correspondence for this and the Donaldson-Thomas instanton on compact Kähler threefolds.