The hypergeometric functions of the Faber-Zagier and Pixton relations
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2015
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910615226810368 |
|---|---|
| author | Buryak, A. Janda, F. Pandharipande, R. |
| author_facet | Buryak, A. Janda, F. Pandharipande, R. |
| contents | The relations in the tautological ring of the moduli space M_g of nonsingular curves conjectured by Faber-Zagier in 2000 and extended to the moduli space of stable pointed curves by Pixton in 2012 are based upon two hypergeometric series A and B. The question of the geometric origins of these series has been solved in at least two ways (via the Frobenius structures associated to 3-spin curves and to CP1). The series A and B also appear in the study of descendent integration on the moduli spaces of open and closed curves. We survey here the various occurrences of A and B starting from their appearance in the asymptotic expansion of the Airy function (calculated by Stokes in the 19th century). Several open questions are proposed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1502_05150 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | The hypergeometric functions of the Faber-Zagier and Pixton relations Buryak, A. Janda, F. Pandharipande, R. Algebraic Geometry Mathematical Physics The relations in the tautological ring of the moduli space M_g of nonsingular curves conjectured by Faber-Zagier in 2000 and extended to the moduli space of stable pointed curves by Pixton in 2012 are based upon two hypergeometric series A and B. The question of the geometric origins of these series has been solved in at least two ways (via the Frobenius structures associated to 3-spin curves and to CP1). The series A and B also appear in the study of descendent integration on the moduli spaces of open and closed curves. We survey here the various occurrences of A and B starting from their appearance in the asymptotic expansion of the Airy function (calculated by Stokes in the 19th century). Several open questions are proposed. |
| title | The hypergeometric functions of the Faber-Zagier and Pixton relations |
| topic | Algebraic Geometry Mathematical Physics |
| url | https://arxiv.org/abs/1502.05150 |