On reduced stable pair invariants
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Author(s)
Oberdieck, Georg B
Date Issued
October 2017
Journal
Mathematische Zeitschrift
Publisher
Springer-Verlag
Citation
Oberdieck, Georg. “On Reduced Stable Pair Invariants.” Mathematische Zeitschrift 289, no. 1–2 (October 20, 2017): 323–353. doi:10.1007/s00209-017-1953-5.
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Author's final manuscript
Abstract
Let X = S × E be the product of a K3 surface S and an elliptic curve E. Reduced stable pair invariants of X can be defined via (1) cutting down the reduced virtual class with incidence conditions or (2) the Behrend function weighted Euler characteristic of the quotient of the moduli space by the translation action of E. We show that (2) arises naturally as the degree of a virtual class, and that the invariants (1) and (2) agree. This has applications to deformation invariance, rationality and a DT/PT correspondence for reduced invariants of S × E.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00209-017-1953-5
