Tropical types and associated cellular resolutions

JOURNAL OF ALGEBRA

卷:356

Article

Dochtermann, Anton²  Joswig, Michael¹  Sanyal, Raman³ 

[1] Tech Univ Darmstadt, Fachbereich Math, D-64293 Darmstadt, Germany

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[3] FU Berlin, Dept Math, D-14195 Berlin, Germany

关键词: Tropical convexity;    Resolutions of monomial ideals;   

DOI  :  10.1016/j.jalgebra.2011.12.028

来源: Elsevier

【 摘 要 】

An arrangement of finitely many tropical hyperplanes in the tropical torus Td-1 leads to a notion of 'type' data for points in Td-1, with the underlying unlabeled arrangement giving rise to 'coarse type'. It is shown that the decomposition of Td-1 induced by types gives rise to minimal cocellular resolutions of certain associated monomial ideals. Via the Cayley trick from geometric combinatorics this also yields cellular resolutions supported on mixed subdivisions of dilated simplices, extending previously known constructions. Moreover, the methods developed lead to an algebraic algorithm for computing the facial structure of arbitrary tropical complexes from point data. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free