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It is a classical fact that sections of a general rational elliptic surface are counted by the coefficients of the Eisenstein series E_4(q). We describe a vast conjectural generalization, associating to any smooth projective variety a quasi-modular form valued in the Chow group of its Kontsevich space of genus 0 stable maps. We provide evidence for this conjecture and draw some consequences from the degree 2 case.