Duke Mathematical Journal

Generating functions for the number of curves on abelian surfaces

Jim Bryan and Naichung Conan Leung
Source: Duke Math. J. Volume 99, Number 2 (1999), 311-328.
First Page: Show Hide
Primary Subjects: 14N10
Secondary Subjects: 11F23, 14J25
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077227774
Mathematical Reviews number (MathSciNet): MR1708022
Zentralblatt MATH identifier: 0976.14033
Digital Object Identifier: doi:10.1215/S0012-7094-99-09911-8

References

[1] Arnaud Beauville, Counting rational curves on $K3$ surfaces, Duke Math. J. 97 (1999), no. 1, 99–108.
Mathematical Reviews (MathSciNet): MR2000c:14073
Zentralblatt MATH: 0999.14018
Digital Object Identifier: doi:10.1215/S0012-7094-99-09704-1
Project Euclid: euclid.dmj/1077228503
[2] J. Bryan and N. C. Leung, The enumerative geometry of $K3$ surfaces and modular forms, preprint, http://xxx.lanl.gov/abs/alg-geom/9711031.
Mathematical Reviews (MathSciNet): MR1750955
Zentralblatt MATH: 0963.14031
Digital Object Identifier: doi:10.1090/S0894-0347-00-00326-X
[3] O. Debarre, On the Euler characteristic of generalized Kummer varieties, preprint, http://xxx.lanl.gov/abs/alg-geom/9711035.
Mathematical Reviews (MathSciNet): MR1738407
Zentralblatt MATH: 0956.14014
Digital Object Identifier: doi:10.1353/ajm.1999.0018
[4] S. K. Donaldson, Yang-Mills invariants of four-manifolds, Geometry of low-dimensional manifolds, 1 (Durham, 1989) eds. S. K. Donaldson and C. B. Thomas, London Math. Soc. Lecture Note Ser., vol. 150, Cambridge Univ. Press, Cambridge, 1990, Gauge Theory and Algebraic Surfaces, pp. 5–40.
Mathematical Reviews (MathSciNet): MR93f:57040
Zentralblatt MATH: 0836.57012
[5] Lothar Göttsche, A conjectural generating function for numbers of curves on surfaces, Comm. Math. Phys. 196 (1998), no. 3, 523–533.
Mathematical Reviews (MathSciNet): MR2000f:14085
Zentralblatt MATH: 0934.14038
Digital Object Identifier: doi:10.1007/s002200050434
[6] Herbert Lange and Christina Birkenhake, Complex abelian varieties, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 302, Springer-Verlag, Berlin, 1992.
Mathematical Reviews (MathSciNet): MR94j:14001
Zentralblatt MATH: 0779.14012
[7] Jun Li and Gang Tian, Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds, Topics in symplectic $4$-manifolds (Irvine, CA, 1996), First Int. Press Lect. Ser., I, Internat. Press, Cambridge, MA, 1998, pp. 47–83.
Mathematical Reviews (MathSciNet): MR2000d:53137
Zentralblatt MATH: 0978.53136
[8] Jun Li and Gang Tian, Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties, J. Amer. Math. Soc. 11 (1998), no. 1, 119–174.
Mathematical Reviews (MathSciNet): MR99d:14011
Zentralblatt MATH: 0912.14004
Digital Object Identifier: doi:10.1090/S0894-0347-98-00250-1
[9] J. Li and G. Tian, Comparison of the algebraic and the symplectic Gromov-Witten invariants, preprint, http://xxx.lanl.gov/abs/alg-geom/9712035.
Mathematical Reviews (MathSciNet): MR1793677
Zentralblatt MATH: 0983.53061
[10] Shing Tung Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math. 31 (1978), no. 3, 339–411.
Mathematical Reviews (MathSciNet): MR81d:53045
Zentralblatt MATH: 0369.53059
Digital Object Identifier: doi:10.1002/cpa.3160310304
[11] Shing-Tung Yau and Eric Zaslow, BPS states, string duality, and nodal curves on $K3$, Nuclear Phys. B 471 (1996), no. 3, 503–512.
Mathematical Reviews (MathSciNet): MR97e:14066
Zentralblatt MATH: 0964.81521
Digital Object Identifier: doi:10.1016/0550-3213(96)00176-9

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