Mixed multiplicities of ideals versus mixed volumes of polytopes
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- by Ngo Viet Trung and Jugal Verma PDF
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Abstract:
The main results of this paper interpret mixed volumes of lattice polytopes as mixed multiplicities of ideals and mixed multiplicities of ideals as Samuel’s multiplicities. In particular, we can give a purely algebraic proof of Bernstein’s theorem which asserts that the number of common zeros of a system of Laurent polynomial equations in the torus is bounded above by the mixed volume of their Newton polytopes.References
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Additional Information
- Ngo Viet Trung
- Affiliation: Institute of Mathematics, Viên Toán Hoc, 18 Hoàng Quôc Viêt, 10307 Hanoi, Vietnam
- MR Author ID: 207806
- Email: nvtrung@math.ac.vn
- Jugal Verma
- Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India 400076
- MR Author ID: 177990
- Email: jkv@math.iitb.ac.in
- Received by editor(s): March 1, 2005
- Received by editor(s) in revised form: March 30, 2005
- Published electronically: May 1, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 4711-4727
- MSC (2000): Primary 52B20, 13D40; Secondary 13H15, 05E99
- DOI: https://doi.org/10.1090/S0002-9947-07-04054-8
- MathSciNet review: 2320648