Abstract
In this paper we compute the Poincaré polynomial of a geometric invariant theory (GIT) quotient of the pointed linear sigma quotient. The pointed linear sigma model is a compactification of the space of degree-d, n-pointed maps from \({\mathbb P^1 \to \mathbb P^r}\) , and carries a natural action of \({G=SL_2(\mathbb C)}\) . Taking a GIT quotient under certain assumptions of n, r, d gives a projective moduli space M and we find its Poincaré polynomial. This M is birational to \({{\overline{M}_{0,n}(\mathbb P^r,d)}}\) and we use this fact to find the Betti numbers of certain stable map spaces.
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Parker, A.E. The Poincaré polynomial of the pointed linear sigma quotient. Beitr Algebra Geom 52, 1–12 (2011). https://doi.org/10.1007/s13366-011-0002-5
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DOI: https://doi.org/10.1007/s13366-011-0002-5