On reduced stable pair invariants
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 tra...
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| Format: | Article |
| Language: | English |
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Springer-Verlag
2018
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| Online Access: | http://hdl.handle.net/1721.1/116224 |
| _version_ | 1826211154695815168 |
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| author | Oberdieck, Georg B |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Oberdieck, Georg B |
| author_sort | Oberdieck, Georg B |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T15:01:26Z |
| format | Article |
| id | mit-1721.1/116224 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:01:26Z |
| publishDate | 2018 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/1162242022-10-02T00:03:11Z On reduced stable pair invariants Oberdieck, Georg B Massachusetts Institute of Technology. Department of Mathematics Oberdieck, Georg B 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. 2018-06-11T18:56:24Z 2018-08-05T05:00:06Z 2017-10 2016-11 2018-05-20T03:43:10Z Article http://purl.org/eprint/type/JournalArticle 0025-5874 1432-1823 http://hdl.handle.net/1721.1/116224 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. en https://doi.org/10.1007/s00209-017-1953-5 Mathematische Zeitschrift 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. Springer-Verlag GmbH Deutschland application/pdf Springer-Verlag Springer Berlin Heidelberg |
| spellingShingle | Oberdieck, Georg B On reduced stable pair invariants |
| title | On reduced stable pair invariants |
| title_full | On reduced stable pair invariants |
| title_fullStr | On reduced stable pair invariants |
| title_full_unstemmed | On reduced stable pair invariants |
| title_short | On reduced stable pair invariants |
| title_sort | on reduced stable pair invariants |
| url | http://hdl.handle.net/1721.1/116224 |
| work_keys_str_mv | AT oberdieckgeorgb onreducedstablepairinvariants |