Tropical types and associated cellular resolutions

详细信息	查看全文 | 推荐本文 |

• 作者：Anton Dochtermann^a ; ¹ ; ^{anton.dochtermann@gmail.com} ; Michael Joswig^b ; ² ; ^{joswig@mathematik.tu-darmstadt.de} ; Raman Sanyal^c ; ³ ; ^{sanyal@math.fu-berlin.de}
• 关键词：Tropical convexity ; Resolutions of monomial ideals
• 刊名：Journal of Algebra
• 出版年：2012
• 期刊代码：69_00218693
• 类别：mt
• 出版时间：15 April, 2012
• 卷：356
• 期：1
• 页码：304-324
• 文件大小：293 K

摘要

An arrangement of finitely many tropical hyperplanes in the tropical torus leads to a notion of 鈥榯ype鈥?data for points in , with the underlying unlabeled arrangement giving rise to 鈥榗oarse type鈥? It is shown that the decomposition of 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.