Homological stability for symmetric complements

Abstract

Conjecture F from [VW12] states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. We prove a generalization of this conjecture to the case of connected manifolds of dimension at least 2 and give an explicit homological stability range.

arXiv comment18 pages. This paper was obtained by combining work of the first two authors (arXiv:1312.6424) and the third author (arXiv:1312.6327). Final version, to appear in Transactions of the American Mathematical Society