Geometry & Topology Volume 13, issue 1 (2009)

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Gromov–Witten invariants of blow-ups along submanifolds with convex normal bundles

Hsin-Hong Lai

Geometry & Topology 13 (2009) 1–48

DOI: 10.2140/gt.2009.13.1

Bibliography

1	K Behrend, Gromov-Witten invariants in algebraic geometry, Invent. Math. 127 (1997) 601 MR1431140
2	K Behrend, B Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997) 45 MR1437495
3	J Bryan, D Karp, The closed topological vertex via the Cremona transform, J. Algebraic Geom. 14 (2005) 529 MR2129009
4	T Coates, A Givental, Quantum Riemann–Roch, Lefschetz and Serre, Ann. of Math. $(2)$ 165 (2007) 15 MR2276766
5	W Fulton, Intersection theory, Ergebnisse der Math. und ihrer Grenzgebiete [Results in Math. and Related Areas] (3) 2, Springer (1984) MR732620
6	W Fulton, R Pandharipande, Notes on stable maps and quantum cohomology, from: "Algebraic geometry—Santa Cruz 1995", Proc. Sympos. Pure Math. 62, Amer. Math. Soc. (1997) 45 MR1492534
7	A Gathmann, Counting rational curves with multiple points and Gromov–Witten invariants of blow-ups arXiv:AG/9609010
8	A Gathmann, Gromov–Witten and degeneration invariants: computation and enumerative significance, PhD thesis, University of Hannover (1998)
9	A Gathmann, Gromov–Witten invariants of blow-ups, J. Algebraic Geom. 10 (2001) 399 MR1832328
10	T Graber, R Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999) 487 MR1666787
11	T Graber, R Vakil, Relative virtual localization and vanishing of tautological classes on moduli spaces of curves, Duke Math. J. 130 (2005) 1 MR2176546
12	J Hu, Gromov–Witten invariants of blow-ups along points and curves, Math. Z. 233 (2000) 709 MR1759269
13	J Hu, Gromov–Witten invariants of blow-ups along surfaces, Compositio Math. 125 (2001) 345 MR1818985
14	J Hu, T J Li, Y Ruan, Birational cobordism invariance of uniruled symplectic manifolds, Invent. Math. 172 (2008) 231 MR2390285
15	E N Ionel, T H Parker, The symplectic sum formula for Gromov–Witten invariants, Ann. of Math. $(2)$ 159 (2004) 935 MR2113018
16	Y H Kiem, J Li, Gromov–Witten invariants of varieties with holomorphic $2$–forms arXiv:0707.2986
17	B Kim, A Kresch, T Pantev, Functoriality in intersection theory and a conjecture of Cox, Katz, and Lee, J. Pure Appl. Algebra 179 (2003) 127 MR1958379
18	A Kresch, Canonical rational equivalence of intersections of divisors, Invent. Math. 136 (1999) 483 MR1695204
19	A Kresch, Cycle groups for Artin stacks, Invent. Math. 138 (1999) 495 MR1719823
20	J Lee, T H Parker, A structure theorem for the Gromov–Witten invariants of Kähler surfaces, J. Differential Geom. 77 (2007) 483 MR2362322
21	A M Li, Y Ruan, Symplectic surgery and Gromov–Witten invariants of Calabi–Yau $3$–folds, Invent. Math. 145 (2001) 151 MR1839289
22	J Li, A degeneration formula of GW–invariants, J. Differential Geom. 60 (2002) 199 MR1938113
23	J Li, G Tian, Virtual moduli cycles and Gromov–Witten invariants of algebraic varieties, J. Amer. Math. Soc. 11 (1998) 119 MR1467172
24	B H Lian, K Liu, S T Yau, Mirror principle. I, Asian J. Math. 1 (1997) 729 MR1621573
25	C H Liu, S T Yau, A degeneration formula of Gromov–Witten invariants with respect to a curve class for degenerations from blow-ups arXiv:math/0408147
26	D Maulik, R Pandharipande, A topological view of Gromov–Witten theory, Topology 45 (2006) 887 MR2248516
27	D McDuff, Hamiltonian $S^1$ manifolds are uniruled arXiv:0706.0675
28	Y Ruan, Surgery, quantum cohomology and birational geometry, from: "Northern California Symplectic Geometry Seminar", Amer. Math. Soc. Transl. Ser. 2 196, Amer. Math. Soc. (1999) 183 MR1736218