We construct new "virtually smooth" modular compactifications of spaces of maps from nonsingular curves to smooth projective toric varieties. They generalize Givental's compactifications, when the complex structure of the curve is allowed to vary and markings are included, and are the toric counterpart of the moduli spaces of stable quotients introduced by Marian, Oprea, and Pandharipande to compactify spaces of maps to Grassmannians. A brief discussion of the resulting invariants and their (conjectural) relation with Gromov-Witten theory is also included.
Bibliographical noteFunding Information:
During the preparation of the paper we have benefited from conversations with Davesh Maulik and Rahul Pandharipande. The material about the big I -function in Section 7 is a joint work with Rahul Pandharipande and we are indebted to him for allowing us to include it in this paper. We also thank Chanzheng Li for pointing out an inaccuracy in earlier version. The research presented here, as well as the writing of the paper, were carried out at the Korea Institute for Advanced Study in Summer 2009. Ciocan-Fontanine thanks KIAS for financial support, excellent working conditions, and an inspiring research environment. Partial support for the research of Ciocan-Fontanine under the NSF grant DMS-0702871 and for the research of Kim under the grant KRF-2007-341-C00006 is gratefully acknowledged.
- Gromov-Witten invariants
- Moduli spaces
- Toric variety