Compactified universal jacobian and the double ramification cycle

Abstract

Using the compactified universal jacobian over the moduli space of stable marked curves, we give an expression in terms of natural classes of the zero section of the compactified universal jacobian the (rational) Chow ring. After extending variants of the Abel-Jacobi map to a locus containing curves of treelike type we give a formula for the pullback of the said zero section along these extensions. The same approach is also applied to recover known formulas for the pullback of theta divisors to the moduli space of marked stable curves.

Added reference. Modifications brought to section 3.4. Comments are welcome!

References in corpus (5)

• Double ramification cycles on the moduli spaces of curves
• The moduli space of twisted canonical divisors
• Equivariant geometry and the cohomology of the moduli space of curves
• Extensions of the universal theta divisor
• Compactifications of the universal Jacobian over curves with marked points

Cited by in corpus (5)

• Extending the Double Ramification Cycle using Jacobians
• Infinitesimal structure of the pluricanonical double ramification locus
• Powers of the theta divisor and relations in the tautological ring
• Compactifications of the universal Jacobian over curves with marked points
• Extensions of the universal theta divisor