2024/09/25 by Javier José Murgas Ibarra, Eirik Eik Svanes, Ibarra, Javier José Murgas +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic and Geometric Analysis #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2409.16524
We review recent results for heterotic moduli and the Hull--Strominger system. In particular, we discuss mathematical properties of the recently derived deformation operator D associated to the deformation complex of heterotic SU(3) solutions. We review results on Serre duality, showing that the operator has a vanishing index, and discuss a notion of Čech cohomology and a particular instance of a Dolbeault theorem for D. Specifically, the cohomology parametrising infinitesimal deformations is isomorphic to the first Čech cohomology of an associated cochain complex. This will be useful for future research, as it provides a more algebraic handle on the heterotic moduli problem, which is useful for understanding notions of stability, geometric invariants, and enumerative geometry for the Hull--Strominger system.