Universal relations on stable map spaces in genus zero
Authors:
Anca M. Mustata and Andrei Mustata
Journal:
Trans. Amer. Math. Soc. 362 (2010), 16991720
MSC (2000):
Primary 14N35, 14F25
Published electronically:
October 28, 2009
MathSciNet review:
2574874
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Abstract: We introduce a factorization for the map between moduli spaces of stable maps which forgets one marked point. This leads to a study of universal relations in the cohomology of stable map spaces in genus zero.
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A. Mustata, A. Mustata, Tautological rings of stable map spaces, preprint.
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 K. Behrend, A. O'Halloran, On the cohomology of stable map spaces, in Invent. Math. 154 (2003), no. 2, 385450. MR 2013785 (2004k:14002)
 [CHS]
 I. Coskun, J. Harris, J. M. Starr, The ample cone of the Kontsevich moduli space, preprint.
 [C1]
 J. Cox, An additive basis for the cohomology ring of , in math.AG/0501322
 [C2]
 J. Cox, A presentation for the cohomology ring in math.AG/0505112
 [FP]
 W. Fulton, R. Pandharipande, Notes on stable maps and quantum cohomology in Algebraic geometry, Santa Cruz 1995, pages 4596, volume 62 of Proc. Symp. Pure Math., Amer. Math. Soc., 1997. MR 1492534 (98m:14025)
 [GP]
 E. Getzler, R. Pandharipande, The Betti numbers of , in math.AG/0502525
 [Has]
 B. Hassett, Moduli spaces of weighted pointed stable curves. Adv. Math. 173 (2003), no. 2, 316352. MR 1957831 (2004b:14040)
 [Ka]
 M. M. Kapranov, Chow quotients of Grassmannians. I, in I. M. Gelfand Seminar, 29110, Adv. Soviet Math., 16, Part 2, Amer. Math. Soc., Providence, RI, 1993. MR 1237834 (95g:14053)
 [Ke]
 S. Keel, Intersection theory of moduli space of stable pointed curves of genus zero, Trans. Amer. Math. Soc. 330 (1992), page 545574. MR 1034665 (92f:14003)
 [KK]
 A. Kabanov, T. Kimura, A change of coordinates on the large phase space of quantum cohomology. Comm. Math. Phys. 217 (2001), no. 1, 107126. MR 1815027 (2002d:14092)
 [LP]
 Y.P. Lee, R. Pandharipande, A reconstruction theorem in quantum cohomology and quantum theory, Amer. J. Math. 126 (2004), no. 6, 13671379. MR 2102400 (2006c:14082)
 [MM1]
 A. Mustata, A. Mustata, Intermediate moduli spaces of stable maps, math.AG/0409569, Invent. Math. 167 (2007), no. 1, 4790 MR 2264804 (2008j:14024)
 [MM2]
 A. Mustata, A. Mustata, The Chow ring of , math.AG/0507464
 [MM3]
 A. Mustata, A. Mustata, Tautological rings of stable map spaces, preprint.
 [MM4]
 A. Mustata, A. Mustata, On Chow quotients, in preparation.
 [O1]
 D. Oprea, The tautological rings of the moduli spaces of stable maps, in math.AG/0404280
 [Pan]
 R. Pandharipande, Intersection of divisors on Kontsevich's Moduli Space and enumerative geometry, Trans. Amer. Math. Soc. 351 (1999), no. 4, 14811505. MR 1407707 (99f:14068)
 [Par]
 A. Parker, An Elementary GIT Construction of the Moduli Space of Stable Maps, in math.AG/0604092
 [W]
 E. Witten, Twodimensional gravity and intersection theory on moduli space. Surveys in differential geometry (Cambridge, MA, 1990), 243310, Lehigh Univ., Bethlehem, PA, 1991. MR 1144529 (93e:32028)
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Additional Information
Anca M. Mustata
Affiliation:
School of Mathematical Sciences, 153 Aras Na Laoi, University College Cork, Cork, Ireland
Email:
A.Mustata@ucc.ie
Andrei Mustata
Affiliation:
School of Mathematical Sciences, 153 Aras Na Laoi, University College Cork, Cork, Ireland
DOI:
http://dx.doi.org/10.1090/S0002994709046066
PII:
S 00029947(09)046066
Received by editor(s):
February 1, 2007
Published electronically:
October 28, 2009
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
