uni-leipzig-open-access/json/s13366-022-00657-9

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We propose a convex algebraic notion of a <jats:italic>patch<\/jats:italic>\u2014a term recently coined by Ciripoi, Kaihnsa, L\u00f6hne, and Sturmfels as a tool for approximating the convex hull of a semi-algebraic set. We discuss geometric consequences, both for the semi-algebraic and convex geometry of the families of faces, as well as variations of our definition and their consequences.<\/jats:p>","DOI":"10.1007\/s13366-022-00657-9","type":"journal-article","created":{"date-parts":[[2022,8,6]],"date-time":"2022-08-06T18:02:48Z","timestamp":1659808968000},"page":"851-875","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Families of faces and the normal cycle of a convex semi-algebraic set"],"prefix":"10.1007","volume":"64","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-3376-6841","authenticated-orcid":false,"given":"Daniel","family":"Plaumann","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0001-9456-6889","authenticated-orcid":false,"given":"Rainer","family":"Sinn","sequence":"additional","affiliation":[]},{"given":"Jannik Lennart","family":"Wesner","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,6]]},"reference":[{"key":"657_CR1","volume-title":"A Course in Convexity. 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