Infinitesimal structure of the pluricanonical double ramification locus

TL;DR

This paper proves that a proposed formula for the pluricanonical double ramification cycle matches a geometrically constructed cycle, using detailed deformation theory analysis.

Contribution

It confirms the validity of a conjectured formula for the pluricanonical double ramification cycle through explicit deformation theory analysis.

Findings

The proposed formula accurately describes the cycle class.

The geometric construction aligns with the formula.

Deformation theory analysis supports the formula's validity.

Abstract

We prove that a formula for the `pluricanonical' double ramification cycle proposed by Janda, Pandharipande, Pixton, Zvonkine, and the second-named author is in fact the class of a cycle constructed geometrically by the first-named author. Our proof proceeds by a detailed explicit analysis of the deformation theory of the double ramification cycle, both to first and to higher order.