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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Enumeration of genus-three plane curves with a fixed complex structure

Author: Aleksey Zinger
Journal: J. Algebraic Geom. 14 (2005), 35-81
Published electronically: May 24, 2004
MathSciNet review: 2092126
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Abstract | References | Additional Information

Abstract: We give a practical formula for counting irreducible nodal genus-three plane curves with a fixed general complex structure on the normalization. As an intermediate step, we enumerate rational plane curves that have a $(3,4)$-cusp.

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Additional Information

Aleksey Zinger
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
Address at time of publication: Department of Mathematics, Stanford University, Stanford, California 94305-2125

Received by editor(s): September 7, 2002
Received by editor(s) in revised form: December 17, 2002
Published electronically: May 24, 2004
Additional Notes: Partially supported by NSF grant DMS-9803166