Abstract We provide families of compact astheno-Kähler nilmanifolds and we study the behaviour complex blowup such manifolds. prove that existence an metric satisfying extra differential condition is not preserved by blowup. also interplay between Strong Kähler with torsion metrics geometrically Bott–Chern metrics. show Fino–Parton–Salamon are geometrically-Bott–Chern-formal, whereas obtain neg...

The unexpected link which is the topic of this article was remarked on by Atiyah himself and his collaborator Raoul Bott in their fundamental 1983 paper [AB83] on the Yang-Mills equations over Riemann surfaces. In this paper Atiyah and Bott used ideas coming from Yang-Mills theory and equivariant Morse theory to derive inductive formulae for the Betti numbers of the moduli spaces M(n, d) of sta...

Given a compact complex manifold $X$ and integrable Beltrami differential $\phi\in A^{0,1}(X, T_{X}^{1,0})$, we introduce double structure on $A^{\bullet,\bullet}(X)$ naturally determined by $\phi$ study its Bott-Chern cohomology. In particular, establish deformation theory for cohomology use it to compute the deformed Iwasawa holomorphically parallelizable Nakamura manifold. The $\partial\bar{...