Relative quasimaps and mirror formulae
We construct and study the theory of relative quasimaps in genus zero, in the spirit of Gathmann. When $X$ is a smooth toric variety and $Y$ is a smooth very ample hypersurface in $X$, we produce a virtual class on the moduli space of relative quasimaps to $(X,Y)$, which we use to define relative qu...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2021
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| In: |
International mathematics research notices
Year: 2021, Issue: 10, Pages: 7885-7931 |
| ISSN: | 1687-0247 |
| DOI: | 10.1093/imrn/rnz339 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1093/imrn/rnz339
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| Author Notes: | Luca Battistella, Navid Nabijou |
| Summary: | We construct and study the theory of relative quasimaps in genus zero, in the spirit of Gathmann. When $X$ is a smooth toric variety and $Y$ is a smooth very ample hypersurface in $X$, we produce a virtual class on the moduli space of relative quasimaps to $(X,Y)$, which we use to define relative quasimap invariants. We obtain a recursion formula which expresses each relative invariant in terms of invariants of lower tangency, and apply this formula to derive a quantum Lefschetz theorem for quasimaps, expressing the restricted quasimap invariants of $Y$ in terms of those of $X$. Finally, we show that the relative $I$-function of Fan-Tseng-You coincides with a natural generating function for relative quasimap invariants, providing mirror-symmetric motivation for the theory. |
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| Item Description: | Gesehen am 04.09.2021 Advance access publication January 22, 2020 |
| Physical Description: | Online Resource |
| ISSN: | 1687-0247 |
| DOI: | 10.1093/imrn/rnz339 |