Acta Mathematica Vietnamica
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$L^p$ Metric Geometry of Big and Nef Cohomology Classes
Eleonora Di Nezza , Chinh H. Lupp. 53-69
Abstract
Let $(X,\omega)$ be a compact Kähler manifold of dimension $n$, and let $\theta$ be a closed smooth real $(1,1)$-form representing a big and nef cohomology class. We introduce a metric $d_p$, $p\ge 1$, on the finite energy space $\mathcal {E}^{p}(X,\theta )$, making it a complete geodesic metric space.