SPEAKER: Sergey Yuzvinsky

TITLE: Split fibers of pencils of hypersurfaces

ABSTRACT In simple terms, we start with two homogeneous complex polynomials F and G of n+1 indeterminates and same degree d>1. Then we consider all their scalar linear combinations aF+bG. Assuming that a generic combination is irreducible, how many completely reducible ones (i.e., products of linear forms) are there? Surprisingly there are strong upper bounds on this number k depending on n regardless of d. For instance k<6 for arbitrary n. Moreover the unions of the divisors of these split combinations can be uniquely characterized by the topological or geometric properties of the complements of their zero loci. The talk will be accessible to students of different math. specialties (and even to their advisors (-:).