3 papers
math.AG2026
Riemann-Roch Polynomials, MBM Classes and Poor IHS Manifolds
Pisya Vikash
We study poor irreducible holomorphic symplectic manifolds, namely those containing no rational curves and no codimension-one subvarieties. We show that, for such manifolds, severa…
math.AG2026
Classification of Smooth Minimal Kähler Fourfolds Without Effective Divisors and Surfaces
Pisya Vikash
We prove that if \(X\) is a compact Kähler fourfold with pseudo--effective canonical bundle and no subvarieties of codimension one or two, then \(K_X\) is a torsion line bundle. By…
math.AG2026
Classification of Poor Manifolds in Low dimensions
Pisya Vikash
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…