Volume 9, issue 2 (2005)

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Counting rational curves of arbitrary shape in projective spaces

Aleksey Zinger

Geometry & Topology 9 (2005) 571–697
Bibliography
1 R Bott, L W Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics 82, Springer (1982) MR658304
2 S Diaz, J Harris, Geometry of the Severi variety, Trans. Amer. Math. Soc. 309 (1988) 1 MR957060
3 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
4 P Griffiths, J Harris, Principles of algebraic geometry, Wiley Classics Library, John Wiley & Sons (1994) MR1288523
5 M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
6 S Katz, Z Qin, Y Ruan, Enumeration of nodal genus-2 plane curves with fixed complex structure, J. Algebraic Geom. 7 (1998) 569 MR1618136
7 M Kontsevich, Y Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994) 525 MR1291244
8 M Kontsevich, Enumeration of rational curves via torus actions, from: "The moduli space of curves (Texel Island, 1994)", Progr. Math. 129, Birkhäuser (1995) 335 MR1363062
9 J Li, G Tian, Virtual moduli cycles and Gromov–Witten invariants of general symplectic manifolds, from: "Topics in symplectic 4–manifolds (Irvine, CA, 1996)", First Int. Press Lect. Ser., I, Int. Press, Cambridge, MA (1998) 47 MR1635695
10 D McDuff, D Salamon, $J$–holomorphic curves and quantum cohomology, University Lecture Series 6, American Mathematical Society (1994) MR1286255
11 R Pandharipande, Intersections of $\mathbb{Q}$–divisors on Kontsevich's moduli space ${M}_{0,n}(\mathbb{P}^r,d)$ and enumerative geometry, Trans. Amer. Math. Soc. 351 (1999) 1481 MR1407707
12 Z Ran, On the quantum cohomology of the plane, old and new, and a $K3$ analogue, Collect. Math. 49 (1998) 519 MR1677096
13 Z Ran, Enumerative geometry of divisorial families of rational curves, Ann. Sc. Norm. Super. Pisa Cl. Sci. $(5)$ 3 (2004) 67 MR2064968
14 Y Ruan, G Tian, A mathematical theory of quantum cohomology, J. Differential Geom. 42 (1995) 259 MR1366548
15 R Vakil, Enumerative geometry of plane curves of low genus arXiv:math.AG/9803007
16 H Zeuthen, Almindelige Egenskaber ved Systemer af Plane Kurver, Kongelige Danske Videnskabernes Selskabs Skrifter 10 (1873) 285
17 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
18 A Zinger, Enumerative vs. symplectic invariants and obstruction bundles, J. Symplectic Geom. 2 (2004) 445 MR2197218
19 A Zinger, Enumeration of genus-three plane curves with a fixed complex structure, J. Algebraic Geom. 14 (2005) 35 MR2092126
20 A Zinger, Enumeration of one-nodal rational curves in projective spaces, Topology 43 (2004) 793 MR2061208