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TitleAlgebraic properties of generic tropical varieties.
Author(s) Tim Römer, Kirsten Schmitz
TypeArticle in Journal
AbstractWe 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 almost-Cohen–Macaulay from the generic tropical variety of I.
Keywordstropical variety, constant coefficient case, Gröbner fan, generic initial ideals, Cohen–Macaulay, multiplicity, depth
ISSN1937-0652; 1944-7833/e
URL http://msp.org/ant/2010/4-4/p03.xhtml
JournalAlgebra Number Theory
PublisherMathematical Sciences Publishers (MSP), Berkeley, CA
Translation No
Refereed No