Browsing by Subject "Generic initial ideals"
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Item Open Access Generic initial ideals of modular polynomial invariants(Elsevier, 2020) Danış, Bekir; Sezer, MüfitWe study the generic initial ideals (gin) of certain ideals that arise in modular invariant theory. For all cases an explicit generating set is known we compute the generic initial ideal of the Hilbert ideal of a cyclic group of prime order for all monomial orders. We also consider the Klein four group and note that its Hilbert ideals are Borel fixed with certain orderings of the variables. In all situations we consider, it is possible to select a monomial order such that the gin of the Hilbert ideal is equal to its initial ideal. Along the way we show that gin respects a permutation of the variables in the monomial order.Item Open Access Generic initial ideals of modular polynomial invariants(Bilkent University, 2020-07) Danış, BekirWe study the generic initial ideals (gin) of certain ideals that arise in modular invariant theory. For all the cases where an explicit generating set is known, we calculate the generic initial ideal of the Hilbert ideal of a cyclic group of prime order for all monomial orders. We also clarify gin for the Klein four group and note that its Hilbert ideals are Borel fixed with certain orderings of the variables. In all the situations we consider, there is a monomial order such that the gin of the Hilbert ideal is equal to its initial ideal. Along the way we show that gin respects a permutation of the variables in the monomial order.Item Open Access A short note on generic initial ideals(TÜBİTAK, 2021-04-19) Danış, BekirThe definition of a generic initial ideal includes the assumption x1 > x2 > · · · > xn . A natural question is how generic initial ideals change when we permute the variables. In the article [1, §2], it is shown that the generic initial ideals are permuted in the same way when the variables in the monomial order are permuted. We give a different proof of this theorem. Along the way, we study the Zariski open sets which play an essential role in the definition of a generic initial ideal and also prove a result on how the Zariski open set changes after a permutation of the variables.