Algebra & Number Theory
- Algebra Number Theory
- Volume 4, Number 4 (2010), 465-491.
Algebraic properties of generic tropical varieties
We show that the algebraic invariants multiplicity and depth of the quotient ring of a polynomial ring and a graded ideal are closely connected to the fan structure of the generic tropical variety of in the constant coefficient case. Generically the multiplicity of 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 from the fan structure of the generic tropical variety of if the depth is known to be greater than . In particular, in this case we can see if is Cohen–Macaulay or almost-Cohen–Macaulay from the generic tropical variety of .
Algebra Number Theory, Volume 4, Number 4 (2010), 465-491.
Received: 11 September 2009
Revised: 5 February 2010
Accepted: 6 April 2010
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]
Secondary: 14Q99: None of the above, but in this section 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
Römer, Tim; Schmitz, Kirsten. Algebraic properties of generic tropical varieties. Algebra Number Theory 4 (2010), no. 4, 465--491. doi:10.2140/ant.2010.4.465. https://projecteuclid.org/euclid.ant/1513729539