Universal relations on stable map spaces in genus zero

Mustaţǎ, Anca; Mustaţǎ, Andrei

doi:10.1090/S0002-9947-09-04606-6

Universal relations on stable map spaces in genus zero
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by Anca M. Mustaţǎ and Andrei Mustaţǎ

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

DOI: https://doi.org/10.1090/S0002-9947-09-04606-6

Published electronically: October 28, 2009

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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.

References

K. Behrend and A. O’Halloran, On the cohomology of stable map spaces, Invent. Math. 154 (2003), no. 2, 385–450. MR 2013785, DOI 10.1007/s00222-003-0308-5
I. Coskun, J. Harris, J. M. Starr, The ample cone of the Kontsevich moduli space, preprint.
J. Cox, An additive basis for the cohomology ring of $\overline {M}_{0,n}(\mathbb {P}^r,2)$, in math.AG/0501322
J. Cox, A presentation for the cohomology ring $H^*(\bar {M}_{0,2}(P^1,2))$ in math.AG/0505112
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, DOI 10.1090/pspum/062.2/1492534
E. Getzler, R. Pandharipande, The Betti numbers of $\overline {M}_{0,n}(r,d)$, in math.AG/0502525
Brendan Hassett, Moduli spaces of weighted pointed stable curves, Adv. Math. 173 (2003), no. 2, 316–352. MR 1957831, DOI 10.1016/S0001-8708(02)00058-0
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
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, DOI 10.1090/S0002-9947-1992-1034665-0
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, DOI 10.1007/s002200000359
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, DOI 10.1353/ajm.2004.0049
Andrei Mustaţă and Magdalena Anca Mustaţă, Intermediate moduli spaces of stable maps, Invent. Math. 167 (2007), no. 1, 47–90. MR 2264804, DOI 10.1007/s00222-006-0006-1
A. Mustata, A. Mustata, The Chow ring of $\overline {M}_{0,m}(n,d)$, math.AG/0507464
A. Mustata, A. Mustata, Tautological rings of stable map spaces, preprint.
A. Mustata, A. Mustata, On Chow quotients, in preparation.
D. Oprea, The tautological rings of the moduli spaces of stable maps, in math.AG/0404280
Rahul Pandharipande, Intersections of $\mathbf Q$-divisors on Kontsevich’s moduli space $\overline M_{0,n}(\mathbf P^r,d)$ and enumerative geometry, Trans. Amer. Math. Soc. 351 (1999), no. 4, 1481–1505. MR 1407707, DOI 10.1090/S0002-9947-99-01909-1
A. Parker, An Elementary GIT Construction of the Moduli Space of Stable Maps, in math.AG/0604092
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