arXiv subjects
Publications and source records attributed to Pisya Vikash.
We prove that if \(X\) is a compact K\"ahler fourfold with pseudo--effective canonical bundle and no subvarieties of codimension one or two, then \(K_X\) is a torsion line bundle. By the Beauville--Bogomolov decomposition theorem, it follows that \(X\) is either a quotient of a complex torus or an irreducible holomorphic symplectic manifold.
The notion of poor manifolds was introduced by Bandman and Zarhin, who asked for their classification. In this paper, we answer this question completely in dimensions at most 3. We also classify poor compact K\"ahler manifolds of arbitrary dimension under the additional assumption that Kodaira dimension is not $-\infty$. We classify all poor $K3$ surfaces. Finally, give a sufficient condition for a compact K\"ahle manifold to have Kodaira dimension greater than or equal to zero.