A Note On Elliptic Plane Curves With Fixed j-Invariant

Abstract

Let N_d be the number of degree d, nodal, rational plane curves through 3d-1 points in the complex projective plane. The number of degree d>=3, nodal, elliptic plane curves with a fixed (general) j-invariant through 3d-1 points is found to be {d-1 \choose 2}*N_d.

10 pages, AMSLatex

References in corpus (1)

• Quantum intersection rings

Cited by in corpus (3)

• Counting embedded curves in symplectic 6-manifolds
• Genus-One Stable Maps, Local Equations, and Vakil-Zinger's desingularization
• Composition law and Nodal genus-2 curves in P^2