Completion of Katz-Qin-Ruan's Enumeration of Genus-Two Plane Curves

2002/01/22 by Aleksey Zinger, A. Zinger, Zinger, A.
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #math.AG #msc:14N99

paper · pdf · doi:10.48550/arxiv.math/0201216

12 pages

arxiv created 2002/01/22 · arxiv updated 2009/11/30

Abstract

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

Related

• Counting plane curves of any genus
• Enumeration of Genus-Three Plane Curves with a Fixed Complex Structure
• Enumeration of Genus-Two Curves with a Fixed Complex Structure in P² and P³
• Enumerative geometry of plane curves of low genus
• Composition law and Nodal genus-2 curves in P²