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Completion of Katz-Qin-Ruan's enumeration of genus-two plane curves

Author(s): Aleksey Zinger
Journal: J. Algebraic Geom. 13 (2004), 547-561.
Posted: December 8, 2003
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Abstract | References | Additional information

Abstract: We give a formula for the number of plane curves of degree $d$ and genus $2$with fixed complex structure passing through $3d-2$ points in general position. This is achieved by completing the Katz-Qin-Ruan approach. This paper's formula agrees with the one obtained by the author in a completely different way.

References:

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E. Ionel, Genus-One Enumerative Invariants in $\mathbb{P}^n$ with Fixed $j$-Invariant, Duke Math. J. 94 (1998), no. 2, 279-324.

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R. Pandharipande, Counting Elliptic Plane Curves with Fixed $j$-Invariant, Proc. Amer. Math. Soc. 125 (1997), no. 12, 3471-3479.

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[V1]
R. Vakil, Enumerative Geometry of Plane Curve of Low Genus, AG/9803007.

[V2]
R. Vakil, A Tool for Stable Reduction of Curves on Surfaces, Advances in Algebraic Geometry Motivated by Physics, 145-154, Amer. Math. Soc., 2001.

[Z]
A. Zinger, Enumeration of Genus-Two Curves with a Fixed Complex Structure in $\mathbb{P}^2$ and $\mathbb{P}^3$, math.SG/0201254.

Additional Information:

Aleksey Zinger
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Rm 2-586, Cambridge, Massachusetts 02139
Address at time of publication: Department of Mathematics, Stanford University, Stanford, California 94305-2125
Email: azinger@math.mit.edu, azinger@math.stanford.edu

PII: S 1056-3911(03)00353-9
Received by editor(s): February 1, 2002
Posted: December 8, 2003
Additional Notes: Partially supported by an NSF Graduate Research Fellowship and NSF grant DMS-9803166

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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