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2010 Algebraic properties of generic tropical varieties
Tim Römer, Kirsten Schmitz
Algebra Number Theory 4(4): 465-491 (2010). DOI: 10.2140/ant.2010.4.465


We show that the algebraic invariants multiplicity and depth of the quotient ring SI of a polynomial ring S and a graded ideal IS are closely connected to the fan structure of the generic tropical variety of I in the constant coefficient case. Generically the multiplicity of SI is shown to correspond directly to a natural definition of multiplicity of cones of tropical varieties. Moreover, we can recover information on the depth of SI from the fan structure of the generic tropical variety of I if the depth is known to be greater than 0. In particular, in this case we can see if SI is Cohen–Macaulay or almost-Cohen–Macaulay from the generic tropical variety of I.


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Tim Römer. Kirsten Schmitz. "Algebraic properties of generic tropical varieties." Algebra Number Theory 4 (4) 465 - 491, 2010.


Received: 11 September 2009; Revised: 5 February 2010; Accepted: 6 April 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1193.13020
MathSciNet: MR2661539
Digital Object Identifier: 10.2140/ant.2010.4.465

Primary: 13F20
Secondary: 13P10, 14Q99

Rights: Copyright © 2010 Mathematical Sciences Publishers


Vol.4 • No. 4 • 2010
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