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Mixed multiplicities of ideals versus mixed volumes of polytopes

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Title Mixed multiplicities of ideals versus mixed volumes of polytopes
 
Creator TRUNG, NV
VERMA, J
 
Subject local-rings
rees-algebras
theorem
mixed volume
mixed multiplicities
multigraded rees algebra
diagonal algebra
toric rings
hilbert functions of multigraded algebras
 
Description 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.
 
Publisher AMER MATHEMATICAL SOC
 
Date 2011-07-16T18:46:17Z
2011-12-26T12:49:54Z
2011-12-27T05:35:43Z
2011-07-16T18:46:17Z
2011-12-26T12:49:54Z
2011-12-27T05:35:43Z
2007
 
Type Article
 
Identifier TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 359(10), 4711-4727
0002-9947
http://dx.doi.org/10.1090/S0002-9947-07-04054-8
http://dspace.library.iitb.ac.in/xmlui/handle/10054/4501
http://hdl.handle.net/10054/4501
 
Language en