Homological stability for symmetric complements

Kupers, Alexander; Miller, Jeremy; Tran, TriThang

doi:10.1090/tran/6623

Homological stability for symmetric complements
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by Alexander Kupers, Jeremy Miller and TriThang Tran PDF

Trans. Amer. Math. Soc. 368 (2016), 7745-7762 Request permission

Abstract:

A conjecture of Vakil and Wood (2015) 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.

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