Socle pairings on tautological rings
<jats:p>We study some aspects of the $\lambda_g$ pairing on the tautological ring of $M_g^c$, the moduli space of genus $g$ stable curves of compact type. We consider pairing kappa classes with pure boundary strata, all tautological classes supported on the boundary, or the full tautologica...
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| Format: | Article |
| Language: | English |
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Centre pour la Communication Scientifique Directe (CCSD)
2022
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| Online Access: | https://hdl.handle.net/1721.1/145828 |
| _version_ | 1826197865314123776 |
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| author | Janda, Felix Pixton, Aaron |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Janda, Felix Pixton, Aaron |
| author_sort | Janda, Felix |
| collection | MIT |
| description | <jats:p>We study some aspects of the $\lambda_g$ pairing on the tautological ring of
$M_g^c$, the moduli space of genus $g$ stable curves of compact type. We
consider pairing kappa classes with pure boundary strata, all tautological
classes supported on the boundary, or the full tautological ring. We prove that
the rank of this restricted pairing is equal in the first two cases and has an
explicit formula in terms of partitions, while in the last case the rank
increases by precisely the rank of the $\lambda_g\lambda_{g - 1}$ pairing on
the tautological ring of $M_g$.</jats:p> |
| first_indexed | 2024-09-23T10:54:41Z |
| format | Article |
| id | mit-1721.1/145828 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:54:41Z |
| publishDate | 2022 |
| publisher | Centre pour la Communication Scientifique Directe (CCSD) |
| record_format | dspace |
| spelling | mit-1721.1/1458282022-10-15T03:32:07Z Socle pairings on tautological rings Janda, Felix Pixton, Aaron Massachusetts Institute of Technology. Department of Mathematics <jats:p>We study some aspects of the $\lambda_g$ pairing on the tautological ring of $M_g^c$, the moduli space of genus $g$ stable curves of compact type. We consider pairing kappa classes with pure boundary strata, all tautological classes supported on the boundary, or the full tautological ring. We prove that the rank of this restricted pairing is equal in the first two cases and has an explicit formula in terms of partitions, while in the last case the rank increases by precisely the rank of the $\lambda_g\lambda_{g - 1}$ pairing on the tautological ring of $M_g$.</jats:p> 2022-10-14T15:02:10Z 2022-10-14T15:02:10Z 2019 2022-10-14T14:50:18Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/145828 Janda, Felix and Pixton, Aaron. 2019. "Socle pairings on tautological rings." Épijournal de Géométrie Algébrique, Volume 3. en 10.46298/EPIGA.2019.VOLUME3.3784 Épijournal de Géométrie Algébrique Creative Commons Attribution-ShareAlike 4.0 International https://creativecommons.org/licenses/by-sa/4.0/ application/pdf Centre pour la Communication Scientifique Directe (CCSD) Épijournal de Géométrie Algébrique |
| spellingShingle | Janda, Felix Pixton, Aaron Socle pairings on tautological rings |
| title | Socle pairings on tautological rings |
| title_full | Socle pairings on tautological rings |
| title_fullStr | Socle pairings on tautological rings |
| title_full_unstemmed | Socle pairings on tautological rings |
| title_short | Socle pairings on tautological rings |
| title_sort | socle pairings on tautological rings |
| url | https://hdl.handle.net/1721.1/145828 |
| work_keys_str_mv | AT jandafelix soclepairingsontautologicalrings AT pixtonaaron soclepairingsontautologicalrings |