Volume 9, issue 4 (2005)

 1 A Beauville, Counting rational curves on $K3$ surfaces, Duke Math. J. 97 (1999) 99 MR1682284 2 J Bryan, N C Leung, The enumerative geometry of $K3$ surfaces and modular forms, J. Amer. Math. Soc. 13 (2000) 371 MR1750955 3 J Bryan, N C Leung, Counting curves on irrational surfaces, from: "Surveys in differential geometry: differential geometry inspired by string theory", Surv. Differ. Geom. 5, Int. Press, Boston (1999) 313 MR1772273 4 X Chen, Rational curves on $K3$ surfaces, J. Algebraic Geom. 8 (1999) 245 MR1675158 5 A Gathmann, The number of plane conics that are five-fold tangent to a given curve, Compos. Math. 141 (2005) 487 MR2134277 6 E Getzler, Topological recursion relations in genus 2, from: "Integrable systems and algebraic geometry (Kobe/Kyoto, 1997)", World Sci. Publ., River Edge, NJ (1998) 73 MR1672112 7 E N Ionel, T H Parker, Relative Gromov–Witten invariants, Ann. of Math. $(2)$ 157 (2003) 45 MR1954264 8 E N Ionel, T H Parker, The symplectic sum formula for Gromov–Witten invariants, Ann. of Math. $(2)$ 159 (2004) 935 MR2113018 9 S Ivashkovich, V Shevchishin, Gromov compactness theorem for $J$–complex curves with boundary, Internat. Math. Res. Notices (2000) 1167 MR1807156 10 A W Knapp, Elliptic curves, Mathematical Notes 40, Princeton University Press (1992) MR1193029 11 M Kontsevich, Y Manin, Relations between the correlators of the topological sigma-model coupled to gravity, Comm. Math. Phys. 196 (1998) 385 MR1645019 12 M Kaneko, D Zagier, A generalized Jacobi theta function and quasimodular forms, from: "The moduli space of curves (Texel Island, 1994)", Progr. Math. 129, Birkhäuser (1995) 165 MR1363056 13 J Lee, Family Gromov–Witten invariants for Kähler surfaces, Duke Math. J. 123 (2004) 209 MR2060027 14 J Lee, Counting curves in elliptic surfaces by symplectic methods, Comm. Anal. Geom. 14 (2006) 107 MR2230572 15 J Lee, N C Leung, Counting elliptic curves in K3 surfaces, J. Algebraic Geom. 15 (2006) 591 MR2237262 16 J Li, A note on enumerating rational curves in a $K3$ surface, from: "Geometry and nonlinear partial differential equations (Hangzhou, 2001)", AMS/IP Stud. Adv. Math. 29, Amer. Math. Soc. (2002) 53 MR1926435 17 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 18 T J Li, A K Liu, Counting curves on elliptic ruled surface, from: "Proceedings of the 1999 Georgia Topology Conference (Athens, GA)" (2002) 347 MR1942426 19 A K Liu, Family blowup formula, admissible graphs and the enumeration of singular curves I, J. Differential Geom. 56 (2000) 381 MR1868322 20 T H Parker, Compactified moduli spaces of pseudo-holomorphic curves, from: "Mirror symmetry, III (Montreal, PQ, 1995)", AMS/IP Stud. Adv. Math. 10, Amer. Math. Soc. (1999) 77 MR1673083 21 T H Parker, J G Wolfson, Pseudo-holomorphic maps and bubble trees, J. Geom. Anal. 3 (1993) 63 MR1197017 22 Y Ruan, G Tian, Higher genus symplectic invariants and sigma models coupled with gravity, Invent. Math. 130 (1997) 455 MR1483992 23 S T Yau, E Zaslow, BPS states, string duality, and nodal curves on $K3$, Nuclear Phys. B 471 (1996) 503 MR1398633