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The Betti numbers of
Author(s):
Ezra
Getzler;
Rahul
Pandharipande
Journal:
J. Algebraic Geom.
15
(2006),
709-732.
Posted:
May 2, 2006
Retrieve article in:
PDF
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.
References:
-
- 1.
- K. Behrend and Yu. Manin, Stacks of stable maps and Gromov-Witten invariants. Duke Math. J. 85 (1996), 1-60. MR 1412436 (98i:14014)
- 2.
- K. Behrend and A. O'Halloran, On the cohomology of stable map spaces, Invent. Math. 154 (2003), 385-450. MR 2013785 (2004k:14002)
- 3.
- J. Cox, An additive basis for the Chow ring of
. math.AG/0501322 - 4.
- V.I. Danilov and A.G. Khovanski
, Newton polyhedra and an algorithm for computing Hodge-Deligne numbers. Math. USSR Izvestiya, 29 (1987), 279-298. - 5.
- P. Deligne, Théorie de Hodge. II. Publ. Math. IHES 40 (1971), 5-58. MR 0498551 (58:16653a)
- 6.
- W. Fulton and R. MacPherson, A compactification of configuration spaces. Ann. Math., 139 (1994), 183-225. MR 1259368 (95j:14002)
- 7.
- W. Fulton and R. Pandharipande, Notes on stable maps and quantum cohomology. In ``Algebraic geometry--Santa Cruz 1995,'' Proc. Sympos. Pure Math., 62, Part 2, Amer. Math. Soc., Providence, RI, 1997, pp. 45-96. MR 1492534 (98m:14025)
- 8.
- E. Getzler, Operads and moduli spaces of genus 0 Riemann surfaces. In ``The moduli space of curves,'' Progr. Math. 129, Birkhäuser Boston, Boston, MA, 1995. MR 1363058 (96k:18008)
- 9.
- E. Getzler, Mixed Hodge structures of configuration spaces. Max-Planck-Institut preprint MPI-96-61. alg-geom/9510018
- 10.
- E. Getzler and M. Kapranov, Modular operads. Compositio Math. 110 (1998), 65-126. MR 1601666 (99f:18009)
- 11.
- 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. MR 1882330 (2002k:14021)
- 12.
- 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. MR 1363062 (97d:14077)
- 13.
- I. G. Macdonald, ``Symmetric Functions and Hall Polynomials.'' Clarendon Press, Oxford, 1995. MR 1354144 (96h:05207)
- 14.
- Yu. I. Manin, Generating functions in algebraic geometry and sums over trees, in ``The moduli space of curves (Texel Island, 1994),'' 401-417, Progr. Math. 129, Birkhäuser Boston, Boston, MA, 1995. MR 363064 (97e:14065)
- 15.
- Yu. Manin, ``Frobenius manifolds, quantum cohomology, and moduli spaces,'' American Mathematical Society Colloquium Publications, 47. American Mathematical Society, Providence, RI, 1999. MR 1702284 (2001g:53156)
- 16.
- A. Mustata and M. Mustata, Intermediate moduli spaces of stable maps. math.AG/0409569
- 17.
- D. Oprea, The tautological rings of the moduli spaces of stable maps. math.AG/0404280
- 18.
- D. Oprea, Tautological classes on the moduli spaces of stable maps to projective spaces. math.AG/0404284
- 19.
- R. Pandharipande, The Chow ring of the non-linear Grassmannian. J. Algebraic Geom. 7 (1998), 123-140. MR 1620694 (99f:14005)
- 20.
- R. Pandharipande, Intersections of
-divisors on Kontsevich's moduli space and enumerative geometry. Trans. Amer. Math. Soc. 351 (1999), 1481-1505. MR 1407707 (99f:14068)
Additional Information:
Ezra
Getzler
Affiliation:
Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730
Email:
getzler@northwestern.edu
Rahul
Pandharipande
Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 08544-1000
Email:
rahulp@math.princeton.edu
PII:
S 1056-3911(06)00425-5
Received by editor(s):
February 26, 2005
Posted:
May 2, 2006
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