Algebraic Geometry Seminar
Given a linear space of dimension 2n, the problem asks to classify complete families of pairwise non-trivially intersecting linear subspaces of dimension $n$. If $n = 2$, it is obvious that such a family consists of two-dimensional subspaces contained in a hyperplane. In 1930 Ugo Morin classified such families in $C^6$ under assumption that they form an irreducible subvariety in the Grassmannian G(3,6). He also raised the question of classification of finite families. I will discuss some recent progress in this direction related to the theory of holomorphic symplectic manifolds.