Volume 12, issue 1 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 29
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
A desingularization of the main component of the moduli space of genus-one stable maps into $\mathbb P^n$

Ravi Vakil and Aleksey Zinger

Geometry & Topology 12 (2008) 1–95
Bibliography
1 M F Atiyah, R Bott, The moment map and equivariant cohomology, Topology 23 (1984) 1 MR721448
2 A Beauville, Quantum cohomology of complete intersections, Mat. Fiz. Anal. Geom. 2 (1995) 384 MR1484335
3 M Bershadsky, S Cecotti, H Ooguri, C Vafa, Holomorphic anomalies in topological field theories, Nuclear Phys. B 405 (1993) 279 MR1240687
4 A Bertram, Another way to enumerate rational curves with torus actions, Invent. Math. 142 (2000) 487 MR1804158
5 C Fontanari, Towards the cohomology of moduli spaces of higher genus stable maps arXiv:math.AG/0611754
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, Absolute and relative Gromov–Witten invariants of very ample hypersurfaces, Duke Math. J. 115 (2002) 171 MR1944571
8 A 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
9 M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
10 K Hori, S Katz, A Klemm, R Pandharipande, R Thomas, C Vafa, R Vakil, E Zaslow, Mirror symmetry, Clay Mathematics Monographs 1, American Mathematical Society (2003) MR2003030
11 M Kontsevich, Y Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994) 525 MR1291244
12 Y P Lee, Quantum Lefschetz hyperplane theorem, Invent. Math. 145 (2001) 121 MR1839288
13 J Li, A Zinger, On the genus-one Gromov-Witten invariants of complete intersections arXiv:math.AG/0507104
14 B H Lian, K Liu, S T Yau, Mirror principle. I, Asian J. Math. 1 (1997) 729 MR1621573
15 D Maulik, R Pandharipande, A topological view of Gromov–Witten theory, Topology 45 (2006) 887 MR2248516
16 R Pandharipande, Intersections of $\mathbf{Q}$–divisors on Kontsevich's moduli space $\overline{M}_{0,n}(\mathbf{P}^r,d)$ and enumerative geometry, Trans. Amer. Math. Soc. 351 (1999) 1481 MR1407707
17 Y Ruan, G Tian, A mathematical theory of quantum cohomology, J. Differential Geom. 42 (1995) 259 MR1366548
18 R Vakil, The enumerative geometry of rational and elliptic curves in projective space, J. Reine Angew. Math. 529 (2000) 101 MR1799935
19 R Vakil, Murphy's law in algebraic geometry: badly-behaved deformation spaces, Invent. Math. 164 (2006) 569 MR2227692
20 R Vakil, A Zinger, A natural smooth compactification of the space of elliptic curves in projective space, Electron. Res. Announc. Amer. Math. Soc. 13 (2007) 53 MR2320682
21 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
22 A Zinger, Enumeration of one-nodal rational curves in projective spaces, Topology 43 (2004) 793 MR2061208
23 A Zinger, Counting rational curves of arbitrary shape in projective spaces, Geom. Topol. 9 (2005) 571 MR2140990
24 A Zinger, A sharp compactness theorem for genus-one pseudo-holomorphic maps arXiv:math.SG/0406103
25 A Zinger, On the structure of certain natural cones over moduli spaces of genus-one holomorphic maps, Adv. Math. 214 (2007) 878 MR2349722
26 A Zinger, Reduced genus-one Gromov-Witten invariants arXiv:math.SG/0507103
27 A Zinger, Intersections of tautological classes on blowups of moduli spaces of genus-one curves, Michigan Math. J. 55 (2007) 535 arXiv:math.AG/0603357
28 A Zinger, The reduced genus-one Gromov-Witten invariants of Calabi-Yau hypersurfaces arXiv:math/0705.2397