{"title":"Explicit rational group law on hyperelliptic Jacobians of any genus","authors":"David Urbanik","doi":"10.4064/ba230330-7-7","DOIUrl":"https://doi.org/10.4064/ba230330-7-7","url":null,"abstract":"It is well-known that abelian varieties are projective, and so there exist explicit polynomial and rational functions which define both the variety and its group law. It is however difficult to find any explicit polynomial and rational functions describin","PeriodicalId":487279,"journal":{"name":"Bulletin of the Polish Academy of Sciences. Mathematics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135783632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Erdős–Dushnik–Miller theorem without AC","authors":"Amitayu Banerjee, Alexa Gopaulsingh","doi":"10.4064/ba221221-6-6","DOIUrl":"https://doi.org/10.4064/ba221221-6-6","url":null,"abstract":"In $mathsf {ZFA}$ (Zermelo–Fraenkel set theory with the Axiom of Extensionality weakened to allow the existence of atoms), we prove that the strength of the proposition $mathsf {EDM}$ (“If $G=(V_{G}, E_{G})$ is a graph such that $V_{G}$ is uncountable,","PeriodicalId":487279,"journal":{"name":"Bulletin of the Polish Academy of Sciences. Mathematics","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135828102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}