The maximum likelihood degree of a very affine variety

By June Huh. Compositio Mathematica, 2012

112 citations recorded by the source corpus.

Abstract We show that the maximum likelihood degree of a smooth very affine variety is equal to the signed topological Euler characteristic. This generalizes Orlik and Terao’s solution to Varchenko’s conjecture on complements of hyperplane arrangements to smooth very affine varieties. For very affine varieties satisfying a genericity condition at infinity, the result is further strengthened to relate the variety of critical points to the Chern–Schwartz–MacPherson class. The strengthened version recovers the geometric deletion–restriction formula of Denham et al. for arrangement complements, and generalizes Kouchnirenko’s theorem on the Newton polytope for nondegenerate hypersurfaces.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5bad402f446c4332531c006d1b6bf3f52d8e3973

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Citations in the corpus

Lagrangian geometry of matroids (2020, methodology): “License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use When M is representable over C,6 the third author gave an algebro-geometric version of Theorem 1.1 in [Huh13].”
Likelihood Geometry (2013, background): “This section ties our discussion to the work of Aluffi [2, 3, 4] and Huh [24, 25, 26].”