{"title":"Deformations of half-canonical Gorenstein curves in codimension four","authors":"Patience Ablett , Stephen Coughlan","doi":"10.1016/j.jsc.2023.102251","DOIUrl":null,"url":null,"abstract":"<div><p>Recent work of Ablett (<span>2021</span>) and Kapustka, Kapustka, Ranestad, Schenck, Stillman and Yuan (<span>2021</span>) outlines a number of constructions for singular Gorenstein codimension four varieties. Earlier work of Coughlan, Gołȩbiowski, Kapustka and Kapustka (<span>2016</span>) details a series of nonsingular Gorenstein codimension four constructions with different Betti tables. In this paper we exhibit a number of flat deformations between Gorenstein codimension four varieties in the same Hilbert scheme, realising many of the singular varieties as specialisations of the earlier nonsingular varieties.</p></div>","PeriodicalId":50031,"journal":{"name":"Journal of Symbolic Computation","volume":"121 ","pages":"Article 102251"},"PeriodicalIF":1.1000,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Symbolic Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0747717123000652","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Recent work of Ablett (2021) and Kapustka, Kapustka, Ranestad, Schenck, Stillman and Yuan (2021) outlines a number of constructions for singular Gorenstein codimension four varieties. Earlier work of Coughlan, Gołȩbiowski, Kapustka and Kapustka (2016) details a series of nonsingular Gorenstein codimension four constructions with different Betti tables. In this paper we exhibit a number of flat deformations between Gorenstein codimension four varieties in the same Hilbert scheme, realising many of the singular varieties as specialisations of the earlier nonsingular varieties.
期刊介绍：
An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects.
It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.
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