Universal relations on stable map spaces in genus zero

Authors:
Anca M. Mustata and Andrei Mustata

Journal:
Trans. Amer. Math. Soc. **362** (2010), 1699-1720

MSC (2000):
Primary 14N35, 14F25

Published electronically:
October 28, 2009

MathSciNet review:
2574874

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[BO]**K. Behrend and A. O’Halloran,*On the cohomology of stable map spaces*, Invent. Math.**154**(2003), no. 2, 385–450. MR**2013785**, 10.1007/s00222-003-0308-5**[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 and R. Pandharipande,*Notes on stable maps and quantum cohomology*, Algebraic geometry—Santa Cruz 1995, Proc. Sympos. Pure Math., vol. 62, Amer. Math. Soc., Providence, RI, 1997, pp. 45–96. MR**1492534**, 10.1090/pspum/062.2/1492534**[GP]**E. Getzler, R. Pandharipande, The Betti numbers of , in math.AG/0502525**[Has]**Brendan Hassett,*Moduli spaces of weighted pointed stable curves*, Adv. Math.**173**(2003), no. 2, 316–352. MR**1957831**, 10.1016/S0001-8708(02)00058-0**[Ka]**M. M. Kapranov,*Chow quotients of Grassmannians. I*, I. M. Gel′fand Seminar, Adv. Soviet Math., vol. 16, Amer. Math. Soc., Providence, RI, 1993, pp. 29–110. MR**1237834****[Ke]**Sean Keel,*Intersection theory of moduli space of stable 𝑛-pointed curves of genus zero*, Trans. Amer. Math. Soc.**330**(1992), no. 2, 545–574. MR**1034665**, 10.1090/S0002-9947-1992-1034665-0**[KK]**Alexandre Kabanov and Takashi Kimura,*A change of coordinates on the large phase space of quantum cohomology*, Comm. Math. Phys.**217**(2001), no. 1, 107–126. MR**1815027**, 10.1007/s002200000359**[LP]**Y.-P. Lee and R. Pandharipande,*A reconstruction theorem in quantum cohomology and quantum 𝐾-theory*, Amer. J. Math.**126**(2004), no. 6, 1367–1379. MR**2102400****[MM1]**Andrei Mustaţă and Magdalena Anca Mustaţă,*Intermediate moduli spaces of stable maps*, Invent. Math.**167**(2007), no. 1, 47–90. MR**2264804**, 10.1007/s00222-006-0006-1**[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]**Rahul Pandharipande,*Intersections of 𝐐-divisors on Kontsevich’s moduli space \overline𝐌_{0,𝐧}(𝐏^{𝐫},𝐝) and enumerative geometry*, Trans. Amer. Math. Soc.**351**(1999), no. 4, 1481–1505. MR**1407707**, 10.1090/S0002-9947-99-01909-1**[Par]**A. Parker, An Elementary GIT Construction of the Moduli Space of Stable Maps, in math.AG/0604092**[W]**Edward Witten,*Two-dimensional gravity and intersection theory on moduli space*, Surveys in differential geometry (Cambridge, MA, 1990) Lehigh Univ., Bethlehem, PA, 1991, pp. 243–310. MR**1144529**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC (2000):
14N35,
14F25

Retrieve articles in all journals with MSC (2000): 14N35, 14F25

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/S0002-9947-09-04606-6

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.