Poincaré polynomials of stable map spaces to grassmannians
López Martín, Alberto
Rendiconti del Seminario Matematico della Università di Padova, Tome 132 (2014), p. 193-208 / Harvested from Numdam
Publié le : 2014-01-01
@article{RSMUP_2014__131__193_0,
     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},
     volume = {132},
     year = {2014},
     pages = {193-208},
     mrnumber = {3217757},
     zbl = {1301.14032},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_2014__131__193_0}
}
López Martín, Alberto. Poincaré polynomials of stable map spaces to grassmannians. Rendiconti del Seminario Matematico della Università di Padova, Tome 132 (2014) pp. 193-208. http://gdmltest.u-ga.fr/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 366940 | Zbl 0275.14007

[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 453766 | Zbl 0355.14015

[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 2013785 | Zbl 1092.14019

[Che01] L. Chen. Poincaré polynomials of hyperquot schemes. Math. Ann., 321(2):235–251, 2001. | MR 1866487 | Zbl 1076.14536

[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 2998922 | Zbl 1282.14026

[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 1492534 | Zbl 0898.14018

[Gat02] A. Gathmann. Absolute and relative Gromov-Witten invariants of very ample hypersurfaces. Duke Math. J., 115(2):171–203, 2002. | MR 1944571 | Zbl 1042.14032

[Gau73] C. F. Gauß. Summatio quarumdam serierum singularium. In Werke. Band II. Georg Olms Verlag, Hildesheim, 1973. Reprint of the 1863 original. | MR 616130

[GP06] E. Getzler and R. Pandharipande. The Betti numbers of M ¯ 0,n (r,d) . J. Algebraic Geom., 15(4):709–732, 2006. | MR 2237267 | Zbl 1114.14032

[KM94] M. Kontsevich and Yu. Manin. Gromov-Witten classes, quantum cohomology, and enumerative geometry. Comm. Math. Phys., 164(3):525–562, 1994. | MR 1291244 | Zbl 0853.14020

[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 1363062 | Zbl 0885.14028

[Man00] Yu. Manin. Stable maps of genus zero flag spaces. Topol. Methods Nonlinear Anal., 11(2):207–217, 1998. | MR 1659474 | Zbl 0987.14033

[Opr06] D. Oprea. Tautological classes on the moduli spaces of stable maps to r via torus actions. Adv. Math., 207(2):661–690, 2006. | MR 2271022 | Zbl 1117.14056

[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 908717 | Zbl 0625.14027