Frontiers of Mathematics in China >
Poincaré polynomials of moduli spaces of stable maps into flag manifolds
Received date: 08 Jul 2016
Accepted date: 29 Jan 2018
Published date: 28 Mar 2018
Copyright
By using the Bialynicki-Birula decomposition and holomorphic Lefschetz formula, we calculate the Poincaré polynomials of the moduli spaces in low degrees.
Key words： Bialynicki-Birula decomposition; Poincaré polynomial
Xiaobo ZHUANG . Poincaré polynomials of moduli spaces of stable maps into flag manifolds[J]. Frontiers of Mathematics in China, 2018 , 13(2) : 483 -508 . DOI: 10.1007/s11464-018-0689-9
| 1 |
Agrawal S. The Euler characteristic of the moduli space of stable maps into a Grassmannian. Undergraduate Thesis, Univ of California, San Diego, 2011
|
| 2 |
Atiyah M F, Singer I M. The index of elliptic operators: III. Ann of Math (2), 1968, 87(3): 546–604
|
| 3 |
Behrend K. Cohomology of stacks. In: Intersection Theory and Moduli. ICTP Lect Notes, Vol 19. 2004, 249–294
|
| 4 |
Bertram A. Quantum schubert calculus. Adv Math, 1997, 128(2): 289–305
|
| 5 |
Bertram A. Towards a Schubert calculus for maps from a Riemann surface to a Grassmannian. Internat J Math, 1994, 5(6): 811–825
|
| 6 |
Bertram A, Ciocan-Fontanine I, Kim B. Two proofs of a conjecture of Hori and Vafa. Duke Math J, 2005, 126(1): 101–136
|
| 7 |
Bialynicki-Birula A. Some theorems on actions of algebraic groups. Ann of Math, 1973, 98(3): 480–497
|
| 8 |
Bialynicki-Birula A. Some properties of the decompositions of algebraic varieties determined by actions of a torus. Bull Acad Polon Sci Sér Sci Math Astronom Phys, 1976, 24(9): 667–674
|
| 9 |
Carrell J B. Torus Actions and Cohomology. In: Gamkrelidze R V, Popov V L, eds. Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action. Encyclopaedia Math Sci, Vol 131. Berlin: Springer, 2002
|
| 10 |
Chen L. Poincaré polynomials of hyperquot schemes. Math Ann, 2001, 321(2): 235–251
|
| 11 |
Ciocan-Fontanine I. On quantum cohomology rings of partial flag varieties. Duke Math J, 1999, 98(3): 485–524
|
| 12 |
Ciocan-Fontanine I. The quantum cohomology ring of flag varieties. Trans Amer Math Soc, 1999, 351(7): 2695–2729
|
| 13 |
Edwards G. On genus zero stable maps to the flag variety. Undergraduate Thesis, Univ of California, San Diego, 2013
|
| 14 |
Fulton W, Pandharipande R. Notes on stable maps and quantum cohomology. arXiv: alg-geom/9608011
|
| 15 |
Hori K. Mirror Symmetry, Vol 1. Providence: Amer Math Soc, 2003
|
| 16 |
Kac V, Cheung P. Quantum Calculus. Berlin: Springer, 2002
|
| 17 |
Kim B. Quot schemes for flags and Gromov invariants for flag varieties. arXiv: alg-geom/9512003
|
| 18 |
Lian B H, Liu C-H, Liu K F, Yau S-T. The S1 fixed points in Quot-schemes and mirror principle computations. In: Cutkosky S D, Edidin D, Qin Z B, Zhang Q, eds. Vector Bundles and Representation Theory. Contemp Math, Vol 322. Providence: Amer Math Soc, 2003, 165–194
|
| 19 |
Manin Yu I. Stable maps of genus zero to flag spaces. Topol Methods Nonlinear Anal, 1998, (2): 207–217
|
| 20 |
Mart´ın A L. Poincaŕe polynomials of stable map spaces to Grassmannians. In: Rendiconti del Seminario Matematico della Universit`a di Padova, Tome 131. 2014, 193–208
|
| 21 |
Oprea D. Tautological classes on the moduli spaces of stable maps to Pr via torus actions. Adv Math, 2006, 207(2): 661–690
|
| 22 |
Skowera J. Bialynicki-Birula decomposition of Deligne-Mumford stacks. Proc Amer Math Soc, 2013, 141(6): 1933–1937
|
| 23 |
Strømme S A. On parametrized rational curves in Grassmann varieties. In: Ghione F, Peskine C, Sernesi E, eds. Space Curves. Lecture Notes in Math, Vol 1266. Berlin: Springer, 1987, 251–272
|
/
| 〈 |
|
〉 |