Characterization of simplices via the Bezout inequality for mixed volumes

Authors:
Christos Saroglou, Ivan Soprunov and Artem Zvavitch

Journal:
Proc. Amer. Math. Soc. **144** (2016), 5333-5340

MSC (2010):
Primary 52A39, 52A40, 52B11

DOI:
https://doi.org/10.1090/proc/13149

Published electronically:
June 10, 2016

MathSciNet review:
3556275

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the following Bezout inequality for mixed volumes:

**[B]**D. N. Bernstein,*The number of roots of a system of equations*, Funkcional. Anal. i Priložen.**9**(1975), no. 3, 1–4 (Russian). MR**0435072****[F]**William Fulton,*Intersection theory*, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 2, Springer-Verlag, Berlin, 1998. MR**1644323****[Kh]**A. G. Hovanskiĭ,*Newton polyhedra, and the genus of complete intersections*, Funktsional. Anal. i Prilozhen.**12**(1978), no. 1, 51–61 (Russian). MR**487230**- [Ku]
A. G. Kushnirenko,
*Newton polyhedra and Bezout's theorem*, (Russian) Funkcional. Anal. i Prilozhen. 10, no. 3, (1976) 82-83. **[Sch]**Rolf Schneider,*Convex bodies: the Brunn-Minkowski theory*, Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge University Press, Cambridge, 1993. MR**1216521**- [SZ]
I. Soprunov and A. Zvavitch,
*Bezout Inequality for Mixed volumes*, arXiv:1507.00765 [math.MG], International Mathematics Research Notices, to appear.

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Additional Information

**Christos Saroglou**

Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44240

Email:
csaroglo@math.kent.edu

**Ivan Soprunov**

Affiliation:
Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115

Email:
i.soprunov@csuohio.edu

**Artem Zvavitch**

Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44240

Email:
zvavitch@math.kent.edu

DOI:
https://doi.org/10.1090/proc/13149

Keywords:
Convex bodies,
mixed volume,
convex polytopes,
Bezout inequality,
Aleksandrov--Fenchel inequality

Received by editor(s):
December 16, 2015

Received by editor(s) in revised form:
February 11, 2016

Published electronically:
June 10, 2016

Additional Notes:
The third author was supported in part by U.S. National Science Foundation Grant DMS-1101636 and by the Simons Foundation.

Communicated by:
Thomas Schlumprecht

Article copyright:
© Copyright 2016
American Mathematical Society