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The nonabelian Hodge correspondence (Corlette-Simpson correspondence), between the polystable Higgs bundles with vanishing Chern classes on a compact Kahler manifold $X$ and the completely reducible flat connections on $X$, is extended to the Fujiki class $mathcal C$ manifolds.
We establish the minimal model theory for $mathbb Q$-factorial log surfaces and log canonical surfaces in Fujikis class $mathcal C$.
In this paper we prove that the cohomology of smooth projective tropical varieties verify the tropical analogs of three fundamental theorems which govern the cohomology of complex projective varieties: Hard Lefschetz theorem, Hodge-Riemann relations
Arising from a topological twist of $mathcal{N} = 4$ super Yang-Mills theory are the Kapustin-Witten equations, a family of gauge-theoretic equations on a four-manifold parametrized by $tinmathbb{P}^1$. The parameter corresponds to a linear combinati
The main problem addressed in the paper is the Torelli problem for n-dimensional varieties of general type, more specifically for varieties with ample canonical bundle. It asks under which geometrical condition for a variety the period map for the Ho
Let $G$ be a reductive group, and let $X$ be an algebraic curve over an algebraically closed field $k$ with positive characteristic. We prove a version of nonabelian Hodge correspondence for $G$-local systems over $X$ and $G$-Higgs bundles over the F