|
Universal relations on stable map spaces in genus zero
Author(s):
Anca
M.
Mustata;
Andrei
Mustata
Journal:
Trans. Amer. Math. Soc.
362
(2010),
1699-1720.
MSC (2000):
Primary 14N35, 14F25
Posted:
October 28, 2009
MathSciNet review:
2574874
Retrieve article in:
PDF
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.
References:
-
- [BO]
- K. Behrend, A. O'Halloran, On the cohomology of stable map spaces, in Invent. Math. 154 (2003), no. 2, 385-450. 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 45-96, 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, 316-352. MR 1957831 (2004b:14040)
- [Ka]
- M. M. Kapranov, Chow quotients of Grassmannians. I, in I. M. Gelfand Seminar, 29-110, 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 545-574. 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, 107-126. 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, 1367-1379. MR 2102400 (2006c:14082) - [MM1]
- A. Mustata, A. Mustata, Intermediate moduli spaces of stable maps, math.AG/0409569, Invent. Math. 167 (2007), no. 1, 47-90 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, 1481-1505. 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, Two-dimensional gravity and intersection theory on moduli space. Surveys in differential geometry (Cambridge, MA, 1990), 243-310, Lehigh Univ., Bethlehem, PA, 1991. MR 1144529 (93e:32028)
Similar Articles:
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:
10.1090/S0002-9947-09-04606-6
PII:
S 0002-9947(09)04606-6
Received by editor(s):
February 1, 2007
Posted:
October 28, 2009
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|