L 2-Betti numbers of plane algebraic curves

Abstract

In (DJL07) it was shown that if A is an ane hyperplane arrangement in C n , then at most one of the L 2 -Betti numbers b (2) (C n A,id) is non-zero. We will prove an analogous statement for complements of any algebraic curve in C 2 . Furthermore we also recast and extend results of (LM06) in terms of L 2 -Betti numbers.