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- W2950113656 abstract "We study the set of circuits of a homogeneous ideal and that of its truncations, and introduce the notion of generic circuits set. We show how this is a well-defined invariant that can be used, in the case of initial ideals with respect to weights, as a counterpart of the (usual) generic initial ideal with respect to monomial orders. As an application we recover the existence of the generic fan introduced by Romer and Schmitz for studying generic tropical varieties. We also consider general initial ideals with respect to weights and show, in analogy to the fact that generic initial ideals are Borel-fixed, that these are fixed under the action of certain Borel subgroups of the general linear group." @default.
- W2950113656 created "2019-06-27" @default.
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- W2950113656 date "2013-09-20" @default.
- W2950113656 modified "2023-09-23" @default.
- W2950113656 title "Generic circuits sets and general initial ideals with respect to weights" @default.
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- W2950113656 doi "https://doi.org/10.1216/jca-2012-4-4-1" @default.
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