The Betti numbers of $\overline {\mathcal {M}}_{0,n}(r,d)$
Authors:
Ezra Getzler and Rahul Pandharipande
Journal:
J. Algebraic Geom. 15 (2006), 709-732
DOI:
https://doi.org/10.1090/S1056-3911-06-00425-5
Published electronically:
May 2, 2006
MathSciNet review:
2237267
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Abstract |
References |
Additional Information
Abstract: We calculate the Betti numbers of the coarse moduli space of stable maps of genus 0 to projective space, using a generalization of the Legendre transform.
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cox J. Cox, An additive basis for the Chow ring of ${\overline {\mathcal {M}}} _{0,n}({\mathbb {P}}^r,2)$. math.AG/0501322
DK V.I. Danilov and A.G. Khovanskiĭ, Newton polyhedra and an algorithm for computing Hodge-Deligne numbers. Math. USSR Izvestiya, 29 (1987), 279–298.
Deligne P. Deligne, Théorie de Hodge. II. Publ. Math. IHES 40 (1971), 5–58.
FM W. Fulton and R. MacPherson, A compactification of configuration spaces. Ann. Math., 139 (1994), 183–225.
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I E. Getzler, Mixed Hodge structures of configuration spaces. Max-Planck-Institut preprint MPI-96-61. alg-geom/9510018
modular E. Getzler and M. Kapranov, Modular operads. Compositio Math. 110 (1998), 65–126.
bp B. Kim and R. Pandharipande, The connectedness of the moduli space of maps to homogeneous spaces. In “Symplectic geometry and mirror symmetry (Seoul, 2000),” 187–201, World Sci. Publishing, River Edge, NJ, 2001.
kont M. Kontsevich, Enumeration of rational curves via torus actions, in “The moduli space of curves (Texel Island, 1994),” 335–368, Progr. Math. 129, Birkhäuser Boston, Boston, MA, 1995.
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manin Yu. Manin, “Frobenius manifolds, quantum cohomology, and moduli spaces,” American Mathematical Society Colloquium Publications, 47. American Mathematical Society, Providence, RI, 1999.
mus A. Mustata and M. Mustata, Intermediate moduli spaces of stable maps. math.AG/0409569
dr1 D. Oprea, The tautological rings of the moduli spaces of stable maps. math.AG/0404280
dr2 D. Oprea, Tautological classes on the moduli spaces of stable maps to projective spaces. math.AG/0404284
rahul:chow R. Pandharipande, The Chow ring of the non-linear Grassmannian. J. Algebraic Geom. 7 (1998), 123–140.
rint R. Pandharipande, Intersections of ${\mathbb {Q}}$-divisors on Kontsevich’s moduli space ${\overline {\mathcal {M}}} _{0,n}({\mathbb {P}}^r,d)$ and enumerative geometry. Trans. Amer. Math. Soc. 351 (1999), 1481–1505.
Additional Information
Ezra Getzler
Affiliation:
Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730
MR Author ID:
210138
ORCID:
0000-0002-5850-7723
Email:
getzler@northwestern.edu
Rahul Pandharipande
Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 08544-1000
MR Author ID:
357813
Email:
rahulp@math.princeton.edu
Received by editor(s):
February 26, 2005
Published electronically:
May 2, 2006
