Irreducibility of Some Nested Hilbert Schemes

Abstract

Let S be a smooth projective surface over C. Let S [n 1 ,...,n k ] denote the nested Hilbert scheme which parametrizes zero-dimensional subschemes ξn 1 ⊂ . . . ⊂ ξn k where ξi is a closed subscheme of S of length i. We show that S [n,m] , S