$L^p$ metric geometry of big and nef cohomology classes

Abstract

Let $(X,\omega )$ be a compact Kähler manifold of dimension $n$, and $\theta$ 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.