2025/06/03 by David Klompenhouwer, Klompenhouwer, David, Stijn Velstra +1
Computer Science · Mathematics · #14H81 #37K10 #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Meromorphic and Entire Functions #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2506.02540
openalex publication_date 2025/06/03 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
We consider strata of curves carrying a residueless meromorphic differential inducing a spin structure on the curve. The cohomology classes of the closures of these strata, weighted by the parity of the spin structures, form a partial cohomological field theory (CohFT) of infinite rank. After applying the DR hierarchy construction to this partial CohFT and reducing to differentials with two zeros and arbitrarily many poles, we show that the resulting system of evolutionary PDEs coincides with the BKP hierarchy up to a coordinate transformation. This is a spin refinement of an analogous result from arXiv:2110.01419. Our proof relies on a new result regarding the reconstruction of the BKP hierarchy from a limited amount of information in the Lax formalism.