2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155832We define an Artin stack which may be considered as a substitute for the non-existing (or empty) moduli space of stable two-pointed curves of genus zero. We show that this Artin stack can be viewed as the first term of a cyclic operad in the category of stacks. Applying the homology functor we obtain a linear cyclic operad. We formulate conjectures which assert that cohomology of a smooth projective variety has the structure of an algebra over this homology operad and that gravitational quantum cohomology can naturally expressed in terms of this algebra. As a test for these conjectures we show how certain well-known relations between gravitational correlators can be deduced from them.Reference added for the formula in Prop. 11.6. Prop 11.7 corrected. Introduction changed accordinglyAlgebraic Geometry14N35; 14H15text