A generalization of the double ramification cycle via log-geometry

Abstract

We give a log-geometric description of the space of twisted canonical divisors constructed by Farkas--Pandharipande. In particular, we introduce the notion of a principal rubber $k$-log-canonical divisor, and we study its moduli space. It is a proper Deligne--Mumford stack admitting a perfect obstruction theory whose virtual fundamental cycle is of dimension $2g-3+n$. In the so-called strictly meromorphic case with $k=1$, the moduli space is of the expected dimension and the push-forward of its virtual fundamental cycle to the moduli space of stable curves equals the weighted fundamental class of the moduli space of twisted canonical divisors. Conjecturally, it yields a formula of Pixton generalizing the double ramification cycle in the moduli space of stable curves.

arXiv comment35 pages

References in corpus (3)

• Double ramification cycles on the moduli spaces of curves
• Logarithmic Geometry and Moduli
• Comparison theorems for Gromov-Witten invariants of smooth pairs and of degenerations

Cited by in corpus (6)

• Logarithmic compactification of the Abel-Jacobi section
• Extending the Double Ramification Cycle using Jacobians
• Infinitesimal structure of the pluricanonical double ramification locus
• Pixton's formula and Abel-Jacobi theory on the Picard stack
• A case study of intersections on blowups of the moduli of curves
• Spin and hyperelliptic structures of log twisted differentials