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Towards the equivariant cohomology ring of moduli spaces of stable maps into Grassmannians Tschirschwitz, Boris


We compute the equivariant hypercohomology of the Koszul complex associated to an equivariant vector field. This hypercohomology is conjectured to be the equivariant cohomology ring of the moduli space M[sub 0,0] (Gr[sub k]C[sup n], 3) of stable maps of degree 3 from genus zero prestable curves into Grassmannians. Our methods are based on the localization methods of E. Alkildis, M . Brion, J.B. Carrell and D.I. Lieberman. This thesis is an extension of the work by K. Behrend and A. O'Halloran on stable maps into projective spaces.

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