2025/10/31 by Dinew, Sławomir, Popovici, Dan · 1 citation
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.27362
Given an n-dimensional compact Kähler manifold, we continue our study of m-positivity in two ways. We first propose generalisations of the notions of pseudo-effective and big Bott-Chern cohomology classes of bidegree (1, 1) by relaxing the standard positivity hypotheses to their m-counterparts after we have proved a Lamari-type duality lemma in bidegree (m, m). Independently, we propose a Monge-Ampère-type non-linear pde whose distinctive feature is that its solutions, if any, are forms of positive degree rather than functions. We prove a form of uniqueness for the solutions and, under the assumption that a solution exists, we give a geometric application involving the m-bigness notion introduced in the first part.