Poincaré polynomials of stable map spaces to grassmannians
Rendiconti del Seminario Matematico della Università di Padova, Tome 131 (2014), pp. 193-208. 
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     author = {L\'opez Mart{\'\i}n, Alberto},
     title = {Poincar\'e polynomials of stable map spaces to grassmannians},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {193--208},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {131},
     year = {2014},
     mrnumber = {3217757},
     zbl = {1301.14032},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2014__131__193_0/}
}
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López Martín, Alberto. Poincaré polynomials of stable map spaces to grassmannians. Rendiconti del Seminario Matematico della Università di Padova, Tome 131 (2014), pp. 193-208. http://www.numdam.org/item/RSMUP_2014__131__193_0/

[BB73] A. Białynicki-Birula. Some theorems on actions of algebraic groups. Ann. of Math. (2), 98:480–497, 1973. | MR | Zbl

[BB76] A. Białynicki-Birula. Some properties of the decompositions of algebraic varieties determined by actions of a torus. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 24(9):667–674, 1976. | MR | Zbl

[Beh] K. Behrend. The Betti numbers of the space of stable maps of genus zero and degree three to the infinite-dimensional Grassmannian. In preparation.

[BO03] K. Behrend and A. O’Halloran. On the cohomology of stable map spaces. Invent. Math., 154(2):385–450, 2003. | MR | Zbl

[Che01] L. Chen. Poincaré polynomials of hyperquot schemes. Math. Ann., 321(2):235–251, 2001. | MR | Zbl

[CHK12] K. Chung, J. Hong and Y-H Kiem. Compactified moduli spaces of rational curves in projective homogeneous varieties. J. Math. Soc. Japan, 64(4):1211–1248, 2012. | MR | Zbl

[FP97] W. Fulton and R. Pandharipande. Notes on stable maps and quantum cohomology. In Algebraic geometry–Santa Cruz 1995, volume 62 of Proc. Sympos. Pure Math., pages 45–96. Amer. Math. Soc., Providence, RI, 1997. | MR | Zbl

[Gat02] A. Gathmann. Absolute and relative Gromov-Witten invariants of very ample hypersurfaces. Duke Math. J., 115(2):171–203, 2002. | MR | Zbl

[Gau73] C. F. Gauß. Summatio quarumdam serierum singularium. In Werke. Band II. Georg Olms Verlag, Hildesheim, 1973. Reprint of the 1863 original. | MR

[GP06] E. Getzler and R. Pandharipande. The Betti numbers of M ¯ 0,n (r,d) . J. Algebraic Geom., 15(4):709–732, 2006. | MR | Zbl

[KM94] M. Kontsevich and Yu. Manin. Gromov-Witten classes, quantum cohomology, and enumerative geometry. Comm. Math. Phys., 164(3):525–562, 1994. | MR | Zbl

[Kon95] M. Kontsevich. Enumeration of rational curves via torus actions. In The moduli space of curves (Texel Island, 1994), volume 129 of Progr. Math., pages 335–368. Birkhäuser Boston, Boston, MA, 1995. | MR | Zbl

[Man00] Yu. Manin. Stable maps of genus zero flag spaces. Topol. Methods Nonlinear Anal., 11(2):207–217, 1998. | MR | Zbl

[Opr06] D. Oprea. Tautological classes on the moduli spaces of stable maps to ℙ r via torus actions. Adv. Math., 207(2):661–690, 2006. | MR | Zbl

[Str87] S. A. Strømme. On parametrized rational curves in Grassmann varieties. In Space curves (Rocca di Papa, 1985), volume 1266 of Lecture Notes in Math., pages 251–272. Springer, Berlin, 1987. | MR | Zbl