On the cohomology of stable map spaces

Abstract

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.

63 pages

Cited by in corpus (10)

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• The Betti numbers of Mbar_{0,n}(r,d)
• The tautological rings of the moduli spaces of stable maps
• Poincaré polynomials of stable map spaces to Grassmannians
• An Additive Basis for the Chow Ring of \bar{M}_{0,2}(P^r,2)
• The dual complex of ${\mathcal{M}}_{1,n}({\mathbb{P}}^r,d)$ via the geometry of the Vakil--Zinger moduli space
• Divisors on the moduli spaces of stable maps to flag varieties and reconstruction
• Moduli space of stable maps to projective space via GIT
• Towards the cohomology of moduli spaces of higher genus stable maps
• A presentation for the Chow ring A^*(\bar{M}_{0,2}(P^1,2))