Genus one enumerative invariants in P^n with fixed j invariant

Abstract

We prove recursive formulas for ${\tau }_d$, the number of degree $d$ elliptic curves with fixed j-invariant in P^n. We use analysis to relate the classical invariant ${\tau }_d$ to the genus one perturbed invariant $R{T}_{1,d}$ defined recently by Ruan and Tian (the later invariant can be computed inductively). By considering a sequence of perturbations converging to zero, we then apply Taubes' Obstruction Bundle method to compute the difference between the two invariants.

LaTeX, 38 pages

References in corpus (1)

• Topological Field Theory and Rational Curves

Cited by in corpus (2)

• Enumeration of Genus-Two Curves with a Fixed Complex Structure in P^2 and P^3
• Genus one enumerative invariants in del-Pezzo surfaces with a fixed complex structure