Lecture - Contraction loci in hyperkähler manifolds

Prof. Misha Verbitsky

Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro (IMPA) and National Research University Higher School of Economics, Moscow

will give a lecture on Contraction loci in hyperkähler manifolds

An MBM curve on a hyperkähler manifold is a rational curve with negative BBF square and minimal possible dimension of its Barlet deformation space. It is known that (up to a possible birational transform) MBM curves survive in all deformations of M which leave its homology class of type (1,1). The MBM locus of an MBM curve is the union of all its deformations in the ambient manifold M. When M is projective, this is a birational contraction locus, and all birational contraction loci are obtained this way (when M is non-projective, a similar result is conjectured). I will prove that all MBM loci in a given deformation class are homeomorphic. This is a joint work with Ekaterina Amerik.