2024/08/25 by Xavier Blot, Paolo Rossi, Blot, Xavier +1 · 2 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2408.13806
openalex publication_date 2024/08/25 · openalex created_date 2024/09/21 · openalex updated_date 2026/07/28
We define twisted versions of the classical and quantum double ramification hierarchy construction based on intersection theory of the strata of meromorphic differentials in the moduli space of stable curves and k-twisted double ramification cycles for k=1, respectively, we prove their integrability and tau symmetry and study their connection. We apply the construction to the case of the trivial cohomological field theory to find it produces the KdV hierarchy, although its relation to the untwisted case is nontrivial. The key role of the KdV hierarchy in controlling the intersection theory of several natural tautological classes translates this relation into a series of remarkable identities between intersection numbers involving psi-classes, Hodge classes, Norbury's theta class and the strata of meromorphic differentials.