The maximum likelihood degree of a very affine variety

  title={The maximum likelihood degree of a very affine variety},
  author={June Huh},
  journal={Compositio Mathematica},
  pages={1245 - 1266}
  • June Huh
  • Published 3 July 2012
  • Mathematics
  • Compositio Mathematica
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… 
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