On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four
L Fu, G Menet - Mathematische Zeitschrift, 2021 - Springer
We extend a result of Guan by showing that the second Betti number of a 4-dimensional
primitively symplectic orbifold is at most 23 and there are at most 91 singular points. The …
primitively symplectic orbifold is at most 23 and there are at most 91 singular points. The …
Topological bounds on hyperkähler manifolds
J Sawon - Experimental Mathematics, 2024 - Taylor & Francis
We conjecture that certain curvature invariants of compact hyperkähler manifolds are
positive/negative. We prove the conjecture in complex dimension four, give an “experimental …
positive/negative. We prove the conjecture in complex dimension four, give an “experimental …
Remarks on Kawamata's effective non-vanishing conjecture for manifolds with trivial first Chern classes
Kawamata proposed a conjecture predicting that every nef and big line bundle on a smooth
projective variety with trivial first Chern class has nontrivial global sections. We verify this …
projective variety with trivial first Chern class has nontrivial global sections. We verify this …
Boundness of for hyperk\"ahler manifolds with vanishing odd-Betti numbers
N Kurnosov - arXiv preprint arXiv:1511.02838, 2015 - arxiv.org
We prove that $ b_2 $ is bounded for hyperk\" ahler manifolds with vanishing odd-Betti
numbers. The explicit upper boundary is conjectured. Following the method described by …
numbers. The explicit upper boundary is conjectured. Following the method described by …