Abstract
We describe the Chow ring with rational coefficients of \(\overline{M}_{0,1}(\mathbb{P}^n,d)\) as the subring of invariants of a ring \(B^*(\overline{M}_{0,1}(\mathbb{P}^n,d);\mathbb{Q})\), relative to the action of the group of symmetries Sd. We compute \(B^*(\overline{M}_{0,1}(\mathbb{P}^n,d);\mathbb{Q})\) by following a sequence of intermediate spaces for \(\overline{M}_{0,1}(\mathbb{P}^n,d)\).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Behrend, K., Fantechi, B.: The intrinsic normal cone. Invent. Math. 128, 45–88 (1997)
Behrend, K., O’Halloran, A.: On the cohomology of stable map spaces. Invent. Math. 154, 385–450 (2003)
Bertram, A.: Another way to enumerate rational curves with torus actions. Invent. Math. 142, 487–512 (2000)
Fulton, W.: Intersection Theory. New York: Springer 1984
Fulton, W., MacPherson, R.: Compactification of configuration space. Ann. Math. 139, 183–225 (1994)
Fulton, W., Pandharipande, R.: Notes on stable maps and quantum cohomology. Algebraic geometry. Santa Cruz 1995, pp. 45–96, vol. 62. Proc. Symp. Pure Math. Providence, RI: American Mathematical Society 1997
Givental, A.: Equivariant Gromov–Witten invariants. Internat. Math. Res. Notices 13, 613-663 (1996)
Graber, T., Kock, J., Pandharipande, R.: Descendant invariants and characteristic numbers. Am. J. Math. 124, 611–647 (2002)
Hartshorne, R.: Algebraic Geometry. New York: Springer, 1977
Hassett, B.: Moduli spaces of weighted pointed stable curves. Adv. Math. 173, 316–352 (2003)
Kapranov, M.M.: Chow quotients of Grassmannians, I. Adv. Soviet Math. 16, 29–110 (1993)
Keel, S.: Intersection theory on moduli space of stable n-pointed genus zero. Trans. Am. Math. Soc. 330, 545–574 (1992)
Knudsen, F.F.: The projectivity of the moduli space of stable curves, II. Math. Scand. 52, 161–199 (1983)
Kontsevich, M., Manin, Y.: Gromov–Witten classes, quantum cohomology, and enumerative geometry. Comm. Math. Phys. 164, 525–562 (1994)
Lian, B.H., Liu, K., Yau, S-T.: Mirror principle, I. Asian J. Math. 1, 729–763 (1997)
Lee, Y.-P., Pandharipande, R.: A reconstruction theorem in quantum cohomology and quantum K-theory. math.AG/0104084
Mustaţǎ, A., Mustaţǎ, A.: On the Chow ring of \(\overline{\textit{M}}_{0,\textit{m}}(\mathbb{P}^\textit{n},\textit{d})\). Am. J. Math. 126, 1367–1373 (2004) math.AG/0507464
Pandharipande, R.: Intersection of \(\mathbb{Q}\)-divisors on Kontsevich’s Moduli Space \(\overline{\textit{M}}_{0,\textit{n}}(\mathbb{P}^\textit{r}, \textit{d})\) and enumerative geometry. Trans. Am. Math. Soc. 351, 1481–1505 (1999)
Thaddeus, M.: Complete collineations revisited. Math. Ann. 315, 469–495 (1999)
Shepard, G.C., Todd, J.A.: Finite unitary reflection groups. Canad. J. Math. 6, 274–304 (1954)
Vistoli, A.: Intersection theory on algebraic stacks and their moduli spaces. Invent. Math. 97, 613–670 (1989)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Mustaţǎ, A., Mustaţǎ, M. Intermediate moduli spaces of stable maps. Invent. math. 167, 47–90 (2007). https://doi.org/10.1007/s00222-006-0006-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00222-006-0006-1