Curve counting in genus one: elliptic singularities and relative geometry
We construct and study the reduced, relative, genus one Gromov-Witten theory of very ample pairs. These invariants form the principal component contribution to relative Gromov-Witten theory in genus one and are relative versions of Zinger’s reduced Gromov-Witten invariants. We relate the relative an...
Guardado en:
| Autores principales: | , , |
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| Formato: | Article (Journal) |
| Lenguaje: | inglés |
| Publicado: |
2021
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| In: |
Algebraic geometry
Year: 2021, Volumen: 8, Número: 6, Pages: 637-679 |
| ISSN: | 2313-1691 |
| DOI: | 10.14231/AG-2021-020 |
| Acceso en línea: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.14231/AG-2021-020 Verlag, lizenzpflichtig, Volltext: http://content.algebraicgeometry.nl/2021-6/2021-6-020.pdf 
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| Notas de Autor: | Luca Battistella, Navid Nabijou and Dhruv Ranganathan |
| Sumario: | We construct and study the reduced, relative, genus one Gromov-Witten theory of very ample pairs. These invariants form the principal component contribution to relative Gromov-Witten theory in genus one and are relative versions of Zinger’s reduced Gromov-Witten invariants. We relate the relative and absolute theories by degeneration of the tangency conditions, and the resulting formulas generalise a well-known recursive calculation scheme put forward by Gathmann in genus zero. The geometric input is a desingularisation of the principal component of the moduli space of genus one logarithmic stable maps to a very ample pair, using the geometry of elliptic singularities. Our study passes through general techniques for calculating integrals on logarithmic blowups of moduli spaces of stable maps, which may be of independent interest. |
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| Notas: | Gesehen am 10.11.2021 |
| Descripción Física: | Online Resource |
| ISSN: | 2313-1691 |
| DOI: | 10.14231/AG-2021-020 |