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Euler Stratifications of Hypersurface Families

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arxiv 2407.18176 v1 pith:HDIM4NCX submitted 2024-07-25 math.AG hep-thmath.STstat.TH

Simon Telen , Maximilian Wiesmann This is my paper · ORCID
classification math.AGhep-thmath.STstat.TH
keywords euleraffinefamilieshypersurfacesstratificationsveryaccordingalgebraic
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We stratify families of projective and very affine hypersurfaces according to their topological Euler characteristic. Our new algorithms compute all strata using algebro-geometric techniques. For very affine hypersurfaces, we investigate and exploit the relation to critical point computations. Euler stratifications are relevant in particle physics and algebraic statistics. They fully describe the dependence of the number of master integrals, respectively the maximum likelihood degree, on kinematic or model parameters.

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  1. The Maximum Likelihood Degree of Toric Models is Monotonic

    math.AG 2025-07 accept novelty 8.0 of 10

    The ML degree is monotone with respect to faces of the defining polytope for scaled toric models, settling a conjecture of Coons and Sullivant.

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