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An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold of K3-type of low dimension using a deformation to a Hilbert scheme of a non-algebraic K3 surface.
An MBM class on a hyperkahler manifold M is a second cohomology class such that its orthogonal complement in H^2(M) contains a maximal dimensional face of the boundary of the Kahler cone for some hyperkahler deformation of M. An MBM curve is a ration
In this paper, we discuss the cycle theory on moduli spaces $cF_h$ of $h$-polarized hyperkahler manifolds. Firstly, we construct the tautological ring on $cF_h$ following the work of Marian, Oprea and Pandharipande on the tautological conjecture on m
The aim of these notes is to acquaint the reader with important objects in complex algebraic geometry: K3 surfaces and their higher-dimensional analogs, hyperkahler manifolds. These manifolds are interesting from several points of view: dynamical (so
Smooth complex polarized varieties $(X,L)$ with a vector subspace $V subseteq H^0(X,L)$ spanning $L$ are classified under the assumption that the locus ${Cal D}(X,V)$ of singular elements of $|V|$ has codimension equal to $dim(X)-i$, $i=3,4,5$, the l
Let V be a convex vector bundle over a smooth projective manifold X, and let Y be the subset of X which is the zero locus of a regular section of V. This mostly expository paper discusses a conjecture which relates the virtual fundamental classes of