In this paper, we introduce the notions of α-Hermitian–Einstein metric and α-stability for I±-
holomorphic vector bundles on bi-Hermitian manifolds. Moreover, we establish a Kobayashi …

Prior works relating meromorphic Higgs bundles to topological recursion, in particular those
of Dumitrescu-Mulase, have considered non-singular models that allow the recursion to be …

It has been observed, by Rayan, that the complex projective surfaces that potentially admit
non-trivial examples of semistable co-Higgs bundles must be found at the lower end of the …

We study the algebraic geometry of twisted Higgs bundles of cyclic type along complex
curves. These objects, which generalize ordinary cyclic Higgs bundles, can be identified …

This thesis is devoted to studying the geometry of holomorphic Poisson brackets on complex
manifolds. We concentrate on the case when the underlying manifold admits a structure of a …

It has been observed by S. Rayan that the complex projective surfaces that potentially admit
non-trivial examples of semistable co-Higgs bundles must be found at the lower end of the …

Homogeneous Higgs and co-Higgs bundles on Hermitian symmetric spaces Page 1 International
Journal of Mathematics Vol. 31, No. 14 (2020) 2050118 (20 pages) c© World Scientific …

Abstract Let (E, ϕ)(E, ϕ) be a rank two co-Higgs vector bundles on a Kähler compact surface
X with ϕ ∈ H^ 0 (X, End (E) ⊗ T_X) ϕ∈ H 0 (X, E nd (E)⊗ TX) nilpotent. If (E, ϕ)(E, ϕ) is …

We study the moduli space MX (Λ, n) of semistable Λ-modules of vanishing Chern classes
over an abelian variety X, where Λ belongs to a certain subclass of D-algebras. In particular …

The purpose of this paper is twofold. We first solve the Dirichlet problem for α-Hermitian–
Einstein equations on I±-holomorphic bundles over bi-Hermitian manifolds. Second, by …