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Homological stability for symmetric complements

Authors: Alexander Kupers, Jeremy Miller and TriThang Tran
Journal: Trans. Amer. Math. Soc. 368 (2016), 7745-7762
MSC (2010): Primary 55R80; Secondary 55R40
Published electronically: December 2, 2015
MathSciNet review: 3546782
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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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Additional Information

Alexander Kupers
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305-2125

Jeremy Miller
Affiliation: Mathematics PhD Program, CUNY Graduate Center, New York, New York 10016-4309
Address at time of publication: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067

TriThang Tran
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222

Received by editor(s): July 14, 2014
Received by editor(s) in revised form: October 20, 2014, and November 12, 2014
Published electronically: December 2, 2015
Additional Notes: The first author was supported by a William R. Hewlett Stanford Graduate Fellowship, Department of Mathematics, Stanford University, and was partially supported by NSF grant DMS-1105058.
Article copyright: © Copyright 2015 American Mathematical Society

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