Battistella, L. and Nabijou, N. (2021) Relative quasimaps and mirror formulae. International Mathematics Research Notices, 2021(10), pp. 7885-7931. (doi: 10.1093/imrn/rnz339)
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Abstract
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.
| Item Type: | Articles |
|---|---|
| Additional Information: | This work was supported by the Royal Society and the Engineering and Physical Sciences Research Council Grants EP/R009325/1 and EP/L015234/1. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Nabijou, Mr Navid |
| Authors: | Battistella, L., and Nabijou, N. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | International Mathematics Research Notices |
| Publisher: | Oxford University Press |
| ISSN: | 1073-7928 |
| ISSN (Online): | 1687-0247 |
| Published Online: | 22 January 2020 |
| Copyright Holders: | Copyright © 2020 The Authors |
| First Published: | First published in International Mathematics Research Notices January 2021(10): 7885-7931 |
| Publisher Policy: | Reproduced under a Creative Commons Licence |
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