{"title":"The symplectic density property for Calogero–Moser spaces","authors":"Rafael B. Andrist, Gaofeng Huang","doi":"10.1112/jlms.70100","DOIUrl":"https://doi.org/10.1112/jlms.70100","url":null,"abstract":"<p>We introduce the symplectic density property and the Hamiltonian density property together with the corresponding versions of Andersén–Lempert theory. We establish these properties for the Calogero–Moser space <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <annotation>$mathcal {C}_n$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> particles and describe its group of holomorphic symplectic automorphisms.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70100","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143475349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Rationality of forms of \u0000 \u0000 \u0000 \u0000 M\u0000 ¯\u0000 \u0000 \u0000 0\u0000 ,\u0000 n\u0000 \u0000 \u0000 $overline{{mathcal {M}}}_{0,n}$","authors":"Brendan Hassett, Yuri Tschinkel, Zhijia Zhang","doi":"10.1112/jlms.70097","DOIUrl":"https://doi.org/10.1112/jlms.70097","url":null,"abstract":"<p>We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143466109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}