Relative quasimaps and mirror formulae

• Verfasst von: Battistella, Luca [VerfasserIn]
• Verfasst von: Nabijou, Navid [VerfasserIn]
• Titel: Relative quasimaps and mirror formulae
• Verf.angabe: Luca Battistella, Navid Nabijou
• Jahr: 2021
• Umfang: 47 S.
• Fussnoten: Gesehen am 04.09.2021 ; Advance access publication January 22, 2020
• Titel Quelle: Enthalten in: International mathematics research notices
• Ort Quelle: Oxford : Oxford University Press, 1991
• Jahr Quelle: 2021
• Band/Heft Quelle: (2021), 10, Seite 7885-7931
• ISSN Quelle: 1687-0247
• DOI: doi:10.1093/imrn/rnz339
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1769435514

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.