{"title":"二阶Calabi-Yau算子","authors":"Gert Almkvist, Duco van Straten","doi":"10.1007/s10801-023-01272-0","DOIUrl":null,"url":null,"abstract":"Abstract We show that the solutions to the equations, defining the so-called Calabi–Yau condition for fourth-order operators of degree two, define a variety that consists of ten irreducible components. These can be described completely in parametric form, but only two of the components seem to admit arithmetically interesting operators. We include a description of the 69 essentially distinct fourth-order Calabi–Yau operators of degree two that are presently known to us.","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"202 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Calabi–Yau operators of degree two\",\"authors\":\"Gert Almkvist, Duco van Straten\",\"doi\":\"10.1007/s10801-023-01272-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We show that the solutions to the equations, defining the so-called Calabi–Yau condition for fourth-order operators of degree two, define a variety that consists of ten irreducible components. These can be described completely in parametric form, but only two of the components seem to admit arithmetically interesting operators. We include a description of the 69 essentially distinct fourth-order Calabi–Yau operators of degree two that are presently known to us.\",\"PeriodicalId\":14926,\"journal\":{\"name\":\"Journal of Algebraic Combinatorics\",\"volume\":\"202 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebraic Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s10801-023-01272-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s10801-023-01272-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Abstract We show that the solutions to the equations, defining the so-called Calabi–Yau condition for fourth-order operators of degree two, define a variety that consists of ten irreducible components. These can be described completely in parametric form, but only two of the components seem to admit arithmetically interesting operators. We include a description of the 69 essentially distinct fourth-order Calabi–Yau operators of degree two that are presently known to us.
期刊介绍：
The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics.
The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.
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