Geodesic
Minimal Gromov--Witten rings
Izvestiya. Mathematics , Tome 72 (2008) no. 6, pp. 1253-1272

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We construct an abstract theory of Gromov–Witten invariants of genus 0 for quantum minimal Fano varieties (a minimal class of varieties which is natural from the quantum cohomological viewpoint). Namely, we consider the minimal Gromov–Witten ring: a commutative algebra whose generators and relations are of the form used in the Gromov–Witten theory of Fano varieties (of unspecified dimension). The Gromov–Witten theory of any quantum minimal variety is a homomorphism from this ring to $\mathbb C$. We prove an abstract reconstruction theorem which says that this ring is isomorphic to the free commutative ring generated by ‘prime two-pointed invariants’. We also find solutions of the differential equation of type $DN$ for a Fano variety of dimension $N$ in terms of the generating series of one-pointed Gromov–Witten invariants. 
@article{IM2_2008_72_6_a6,
     author = {V. V. Przyjalkowski},
     title = {Minimal {Gromov--Witten} rings},
     journal = {Izvestiya. Mathematics },
     pages = {1253--1272},
     publisher = {mathdoc},
     volume = {72},
     number = {6},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2008_72_6_a6/}
}
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V. V. Przyjalkowski. Minimal Gromov--Witten rings. Izvestiya. Mathematics , Tome 72 (2008) no. 6, pp. 1253-1272. http://geodesic.mathdoc.fr/item/IM2_2008_72_6_a6/