On the cohomology of stable map spaces

Details On the cohomology of stable map spaces On the cohomology of stable map spaces

2002-02-27

arxiv.org/abs/math/0202288v1

Mathematics

Algebraic Geometry

63 pages

Scientific paper

We describe an approach to calculating the cohomology rings of stable map spaces. The method we use is due to Akildiz-Carrell and employs a C^*-action and a vector field which is equivariant with respect to this C^*-action. We give an explicit description of the big Bialynicky-Birula cell of the C^*-action on Mbar_00(P^n,d) as a vector bundle on Mbar_0d. This is used to calculate explicitly the cohomology ring of Mbar_00(P^n,d) in the cases d=2 and d=3. Of particular interest is the case as n approaches infinity.

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