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A. Zinger defined reduced Gromov-Witten (GW) invariants and proved acomparison theorem of standard and reduced genus one GW invariants for everysymplectic manifold (with all dimension). H. -L. Chang and J. Li provided aproof of the comparison theorem for quintic Calabi-Yau 3-folds in algebraicgeometry by taking a definition of reduced invariants as an Euler number ofcertain vector bundle. T. Coates and C. Manolache have defined reduced GWinvariants in algebraic geometry following the idea by Vakil and Zinger andproved the comparison theorem for every Calabi-Yau threefold. In this paper, weprove the comparison theorem for every (not necessarily Calabi-Yau) completeintersection of dimension 2 or 3 in projective spaces by taking a definition ofreduced GW invariants in the paper of Coates and Manolache.

Algebraic reduced genus one Gromov-Witten invariants for complete intersections in projective spaces