Geometry & Topology Volume 13, issue 5 (2009)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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A sharp compactness theorem for genus-one pseudo-holomorphic maps

Aleksey Zinger

Geometry & Topology 13 (2009) 2427–2522

DOI: 10.2140/gt.2009.13.2427

Bibliography

1	K Behrend, B Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997) 45 MR1437495
2	M Bershadsky, S Cecotti, H Ooguri, C Vafa, Holomorphic anomalies in topological field theories, Nuclear Phys. B 405 (1993) 279 MR1240687
3	A Floer, H Hofer, D Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. J. 80 (1995) 251 MR1360618
4	K Fukaya, K Ono, Arnold conjecture and Gromov–Witten invariant, Topology 38 (1999) 933 MR1688434
5	E Ionel, Genus $1$ enumerative invariants in $\mathbf P^n$ with fixed $j$ invariant, Duke Math. J. 94 (1998) 279 MR1638587
6	J Li, G Tian, Virtual moduli cycles and Gromov–Witten invariants of general symplectic manifolds, from: "Topics in symplectic $4$–manifolds (Irvine, CA, 1996)" (editor R J Stern), First Int. Press Lect. Ser. I, Int. Press (1998) 47 MR1635695
7	J Li, A Zinger, On the genus-one Gromov–Witten invariants of complete intersections, to appear in J. Diff. Geom. arXiv:math/0507104
8	D McDuff, D Salamon, $J$–holomorphic curves and quantum cohomology, Univ. Lecture Series 6, Amer. Math. Soc. (1994) MR1286255
9	Y Ruan, G Tian, A mathematical theory of quantum cohomology, J. Differential Geom. 42 (1995) 259 MR1366548
10	Y Ruan, G Tian, Higher genus symplectic invariants and sigma models coupled with gravity, Invent. Math. 130 (1997) 455 MR1483992
11	R Vakil, A tool for stable reduction of curves on surfaces, from: "Advances in algebraic geometry motivated by physics (Lowell, MA, 2000)" (editor E Previato), Contemp. Math. 276, Amer. Math. Soc. (2001) 145 MR1837115
12	R Vakil, A Zinger, A desingularization of the main component of the moduli space of genus-one stable maps into $\mathbb P^n$, Geom. Topol. 12 (2008) 1 MR2377245
13	A Zinger, Enumeration of genus-two curves with a fixed complex structure in $\mathbb P^2$ and $\mathbb P^3$, J. Differential Geom. 65 (2003) 341 MR2064428
14	A Zinger, Basic estimates of riemannian geometry used in gluing pseudoholomorphic maps, Notes (2004)
15	A Zinger, Completion of Katz–Qin–Ruan's enumeration of genus-two plane curves, J. Algebraic Geom. 13 (2004) 547 MR2047680
16	A Zinger, Enumerative vs. symplectic invariants and obstruction bundles, J. Symplectic Geom. 2 (2004) 445 MR2197218
17	A Zinger, Counting rational curves of arbitrary shape in projective spaces, Geom. Topol. 9 (2005) 571 MR2140990
18	A Zinger, On the structure of certain natural cones over moduli spaces of genus-one holomorphic maps, Adv. Math. 214 (2007) 878 MR2349722
19	A Zinger, Reduced genus-one Gromov–Witten invariants arXiv:math/0507103
20	A Zinger, Pseudocycles and integral homology, Trans. Amer. Math. Soc. 360 (2008) 2741 MR2373332
21	A Zinger, Standard versus reduced genus-one Gromov–Witten invariants, Geom. Topol. 12 (2008) 1203 MR2403808
22	A Zinger, The reduced genus-one Gromov–Witten invariants of Calabi–Yau hypersurfaces, J. Amer. Math. Soc. 22 (2009) 691