Stable maps to rational curves and the relative Jacobian

Abstract

We consider two cycles on the moduli space of compact type curves and prove that they coincide. The first is defined by pushing forward the virtual fundamental classes of spaces of relative stable maps to an unparameterized rational curve, while the second is obtained as the intersection of the Abel section of the universal Jacobian with the zero section. Our comparison extends results of Cavalieri-Marcus-Wise where the same identity was proved over on the locus of rational tails curves.

11 pages

References in corpus (3)

• Normal Functions and the Geometry of Moduli Spaces of Curves
• The moduli space of curves, double Hurwitz numbers, and Faber's intersection number conjecture
• Expanded degenerations and pairs

Cited by in corpus (10)

• Double ramification cycles and integrable hierarchies
• Pixton's double ramification cycle relations
• Double ramification cycles with target varieties
• Logarithmic compactification of the Abel-Jacobi section
• Pixton's formula and Abel-Jacobi theory on the Picard stack
• Powers of the theta divisor and relations in the tautological ring
• Compactifications of the universal Jacobian over curves with marked points
• Compactified universal jacobian and the double ramification cycle
• Extended $r$-spin theory in all genera and the discrete KdV hierarchy
• Tropical double ramification loci