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Maximum likelihood degree of Fermat hypersurfaces via Euler characteristics


Author: Botong Wang
Journal: Proc. Amer. Math. Soc. 144 (2016), 3649-3655
MSC (2010): Primary 14Q10; Secondary 32S50
DOI: https://doi.org/10.1090/proc/13127
Published electronically: May 4, 2016
MathSciNet review: 3513528
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Abstract: Maximum likelihood degree of a projective variety is the number of critical points of a general likelihood function. In this note, we compute the maximum likelihood degree of Fermat hypersurfaces. We give a formula of the maximum likelihood degree in terms of the constants $ \beta _{\mu , \nu }$, which is defined to be the number of complex solutions to the system of equations $ z_1^\nu =z_2^\nu =\cdots =z_\mu ^\nu =1$ and $ z_1+\cdots +z_\mu +1=0$.


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Additional Information

Botong Wang
Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
Email: wang@math.wisc.edu

DOI: https://doi.org/10.1090/proc/13127
Received by editor(s): September 24, 2015
Published electronically: May 4, 2016
Communicated by: Lev Borisov
Article copyright: © Copyright 2016 American Mathematical Society

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