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In 1989, Ziegler showed that the restriction \n \n $${{\\mathscr {A}}}''$$<\/jats:tex-math>\n \n \n \n A<\/mml:mi>\n <\/mml:mrow>\n \n \u2032<\/mml:mo>\n \u2032<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> of \n \n $${{\\mathscr {A}}}$$<\/jats:tex-math>\n \n A<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> to any hyperplane endowed with the natural multiplicity \n \n $$\\kappa $$<\/jats:tex-math>\n \n \u03ba<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> is then a free multiarrangement \n \n $$({{\\mathscr {A}}}'',\\kappa )$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n \n \n A<\/mml:mi>\n <\/mml:mrow>\n \n \u2032<\/mml:mo>\n \u2032<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msup>\n ,<\/mml:mo>\n \u03ba<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>. The aim of this paper is to prove an analogue of Ziegler\u2019s theorem for the stronger notion of inductive freeness: if \n \n $${{\\mathscr {A}}}$$<\/jats:tex-math>\n \n A<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> is inductively free, then so is the multiarrangement \n \n $$({{\\mathscr {A}}}'',\\kappa )$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n \n \n A<\/mml:mi>\n <\/mml:mrow>\n \n \u2032<\/mml:mo>\n \u2032<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msup>\n ,<\/mml:mo>\n \u03ba<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>. In a related result we derive that if a deletion \n \n $${{\\mathscr {A}}}'$$<\/jats:tex-math>\n \n \n \n A<\/mml:mi>\n <\/mml:mrow>\n \u2032<\/mml:mo>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> of \n \n $${{\\mathscr {A}}}$$<\/jats:tex-math>\n \n A<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> is free and the corresponding restriction \n \n $${{\\mathscr {A}}}''$$<\/jats:tex-math>\n \n \n \n A<\/mml:mi>\n <\/mml:mrow>\n \n \u2032<\/mml:mo>\n \u2032<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> is inductively free, then so is \n \n $$({{\\mathscr {A}}}'',\\kappa )$$<\/jats:tex-math>\n \n \n (<\/mml:mo>\n \n \n A<\/mml:mi>\n <\/mml:mrow>\n \n \u2032<\/mml:mo>\n \u2032<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msup>\n ,<\/mml:mo>\n \u03ba<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\u2014irrespective of the freeness of \n \n $${{\\mathscr {A}}}$$<\/jats:tex-math>\n \n A<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>. In addition, we show counterparts of the latter kind for additive and recursive freeness.<\/jats:p>","DOI":"10.1007\/s00454-024-00644-y","type":"journal-article","created":{"date-parts":[[2024,4,21]],"date-time":"2024-04-21T18:01:16Z","timestamp":1713722476000},"page":"528-549","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Inductive Freeness of Ziegler\u2019s Canonical Multiderivations"],"prefix":"10.1007","volume":"73","author":[{"given":"Torsten","family":"Hoge","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8165-529X","authenticated-orcid":false,"given":"Gerhard","family":"R\u00f6hrle","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,21]]},"reference":[{"issue":"1","key":"644_CR1","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/s00222-015-0615-7","volume":"204","author":"T Abe","year":"2016","unstructured":"Abe, T.: Divisionally free arrangements of hyperplanes. 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