Twisted cohomology and likelihood ideals
A likelihood function on a smooth very affine variety gives rise to a twisted de Rham complex. We show how its top cohomology vector space degenerates to the coordinate ring of the critical points defined by the likelihood equations. We obtain a basis for cohomology from a basis of this coordinate ring. We investigate the dual picture, where twisted cycles correspond to critical points. We show how to expand a twisted cocycle in terms of a basis, and apply our methods to Feynman integrals from physics.
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Matsubara-Heo, S, & Telen, S.J.L. (2023). Twisted cohomology and likelihood ideals. doi:10.48550/arXiv.2301.13579