2023/11/01 by Popovici, Dan, Ugarte, Luis
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2311.00485
Given a complex balanced manifold X and a compact complex manifold S equipped with a positive volume form dV>0 and satisfying an extra condition such that dim S\geqdim X -1, we construct a moment map for the action of the Lie group of biholomorphisms of S that preserve dV onto the space of holomorphic maps f:S\longrightarrow X that satisfy a certain condition with respect to the Bott-Chern cohomology class of the balanced metric of X. The purpose is twofold: to study such maps as a possible addition to some very recent hyperbolicity notions involving holomorphic maps with a certain type of growth from some \Cp, rather than S, to X; and to lay the groundwork for a possible future construction of balanced quotients as an analogue of the classical symplectic quotients.