Details:
Title  Algebraic properties of generic tropical varieties.  Author(s)  Tim Römer, Kirsten Schmitz  Type  Article in Journal  Abstract  We show that the algebraic invariants multiplicity and depth of the quotient ring S∕I of a polynomial ring S and a graded ideal I⊂S are closely connected to the fan structure of the generic tropical variety of I in the constant coefficient case. Generically the multiplicity of S∕I 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 S∕I 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 S∕I is Cohen–Macaulay or almostCohen–Macaulay from the generic tropical variety of I.  Keywords  tropical variety, constant coefficient case, Gröbner fan, generic initial ideals, Cohen–Macaulay, multiplicity, depth  ISSN  19370652; 19447833/e 
URL 
http://msp.org/ant/2010/44/p03.xhtml 
Language  English  Journal  Algebra Number Theory  Volume  4  Number  4  Pages  465491  Publisher  Mathematical Sciences Publishers (MSP), Berkeley, CA  Year  2010  Edition  0  Translation 
No  Refereed 
No 
