Geometry & Topology Volume 18, issue 2 (2014)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

The genus $0$ Gromov–Witten invariants of projective complete intersections

Aleksey Zinger

Geometry & Topology 18 (2014) 1035–1114

DOI: 10.2140/gt.2014.18.1035

Bibliography

1	T M Apostol, Calculus, Vol. II: Multi-variable calculus and linear algebra, with applications to differential equations and probability, Blaisdell Publishing (1969) MR0248290
2	M Artin, Algebra, Prentice Hall (1991) MR1129886
3	M F Atiyah, R Bott, The moment map and equivariant cohomology, Topology 23 (1984) 1 MR721448
4	S Barannikov, Generalized periods and mirror symmetry in dimensions $n\gt 3$, arXiv:math/9903124
5	A Bertram, Another way to enumerate rational curves with torus actions, Invent. Math. 142 (2000) 487 MR1804158
6	A Bertram, H P Kley, New recursions for genus-zero Gromov–Witten invariants, Topology 44 (2005) 1 MR2103998
7	P Candelas, X C de la Ossa, P S Green, L Parkes, A pair of Calabi–Yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B 359 (1991) 21 MR1115626
8	L Cherveny, Genus-zero mirror principle with two marked points, arXiv:1001.0242
9	P Di Francesco, C Itzykson, Quantum intersection rings, from: "RCP 25, Vol. 46" (editors R Dijkgraaf, C Faber, G van der Geer), Prépubl. Inst. Rech. Math. Av. 1994/29, Univ. Louis Pasteur (1994) 153 MR1331616
10	G Ellingsrud, S A Strømme, Bott's formula and enumerative geometry, J. Amer. Math. Soc. 9 (1996) 175 MR1317230
11	A Gathmann, Absolute and relative Gromov–Witten invariants of very ample hypersurfaces, Duke Math. J. 115 (2002) 171 MR1944571
12	A B Givental, Equivariant Gromov–Witten invariants, Internat. Math. Res. Notices (1996) 613 MR1408320
13	A B Givental, The mirror formula for quintic threefolds, from: "Northern California Symplectic Geometry Seminar", Amer. Math. Soc. Transl. Ser. 2 196, Amer. Math. Soc. (1999) 49 MR1736213
14	A B Givental, Semisimple Frobenius structures at higher genus, Internat. Math. Res. Notices (2001) 1265 MR1866444
15	B R Greene, D R Morrison, M R Plesser, Mirror manifolds in higher dimension, from: "Mirror symmetry, II" (editors B Greene, S T Yau), AMS/IP Stud. Adv. Math. 1, Amer. Math. Soc. (1997) 745 MR1416356
16	P Griffiths, J Harris, Principles of algebraic geometry, Wiley Classics Library, Wiley (1994) MR1288523
17	K Hori, S Katz, A Klemm, R Pandharipande, R Thomas, C Vafa, R Vakil, E Zaslow, Mirror symmetry, Clay Mathematics Monographs 1, Amer. Math. Soc. (2003) MR2003030
18	S Katz, Rational curves on Calabi–Yau manifolds: Verifying predictions of mirror symmetry, from: "Projective geometry with applications" (editor E Ballico), Lecture Notes in Pure and Appl. Math. 166, Dekker (1994) 231 MR1302954
19	A Klemm, R Pandharipande, Enumerative geometry of Calabi–Yau $4$–folds, Comm. Math. Phys. 281 (2008) 621 MR2415462
20	Y P Lee, Quantum Lefschetz hyperplane theorem, Invent. Math. 145 (2001) 121 MR1839288
21	Y P Lee, R Pandharipande, A reconstruction theorem in quantum cohomology and quantum $K$–theory, Amer. J. Math. 126 (2004) 1367 MR2102400
22	B H Lian, K Liu, S T Yau, Mirror principle, I, Asian J. Math. 1 (1997) 729 MR1621573
23	D Maulik, R Pandharipande, in progress
24	D Maulik, R Pandharipande, A topological view of Gromov–Witten theory, Topology 45 (2006) 887 MR2248516
25	D McDuff, D Salamon, $J$–holomorphic curves and symplectic topology, AMS Colloquium Publications 52, Amer. Math. Soc. (2004) MR2045629
26	A Popa, The genus one Gromov–Witten invariants of Calabi–Yau complete intersections, Trans. Amer. Math. Soc. 365 (2013) 1149 MR3003261
27	A Popa, A Zinger, Mirror symmetry for closed, open, and unoriented Gromov–Witten invariants, arXiv:1010.1946
28	Y Ruan, G Tian, A mathematical theory of quantum cohomology, J. Differential Geom. 42 (1995) 259 MR1366548
29	D Zagier, A Zinger, Some properties of hypergeometric series associated with mirror symmetry, from: "Modular forms and string duality" (editors N Yui, H Verrill, C F Doran), Fields Inst. Commun. 54, Amer. Math. Soc. (2008) 163 MR2454324
30	A Zinger, Genus–zero two–point hyperplane integrals in the Gromov–Witten theory, Comm. Anal. Geom. 17 (2009) 955 MR2643736
31	A Zinger, The reduced genus $1$ Gromov–Witten invariants of Calabi–Yau hypersurfaces, J. Amer. Math. Soc. 22 (2009) 691 MR2505298