Locally nilpotent derivations and automorphism groups of certain Danielewski surfaces

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• 作者：Angelo Calil Bianchi^a ; ¹ ; ^{acbianchi@unifesp.br" class="auth_mail" title="E-mail the corresponding author} ; Marcelo Oliveira Veloso^b ; ^{veloso@ufsj.edu.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：13N15 ; 14R10
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：469
• 期：Complete
• 页码：96-108
• 全文大小：362 K

文摘

We describe the set of all locally nilpotent derivations of the quotient ring class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302873&_mathId=si1.gif&_user=111111111&_pii=S0021869316302873&_rdoc=1&_issn=00218693&md5=b8c33e68548b9bfab7285128380deed0" title="Click to view the MathML source">K[X,Y,Z]/(f(X)Y−φ(X,Z))class="mathContainer hidden">class="mathCode">$\mathbb{K}[X,Y,Z]/(f(X)Y-\phi (X,Z))$ constructed from the defining equation class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302873&_mathId=si2.gif&_user=111111111&_pii=S0021869316302873&_rdoc=1&_issn=00218693&md5=0a82e2d43b3c36cd52d0fb94c73b504f" title="Click to view the MathML source">f(X)Y=φ(X,Z)class="mathContainer hidden">class="mathCode">$f(X)Y=\phi (X,Z)$ of a generalized Danielewski surface   in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302873&_mathId=si3.gif&_user=111111111&_pii=S0021869316302873&_rdoc=1&_issn=00218693&md5=bd639341809b33aaff6c3f1a7d2e49e5" title="Click to view the MathML source">K³class="mathContainer hidden">class="mathCode">${\mathbb{K}}^3$ for a specific choice of polynomials f and φ  , with class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302873&_mathId=si4.gif&_user=111111111&_pii=S0021869316302873&_rdoc=1&_issn=00218693&md5=6f62ed0002316ca6e6358ef5be39b65d" title="Click to view the MathML source">Kclass="mathContainer hidden">class="mathCode">$\mathbb{K}$ an algebraically closed field of characteristic zero. As a consequence of this description we calculate the ML  -invariant and the Derksen invariant of this ring. We also determine a set of generators for the group of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302873&_mathId=si4.gif&_user=111111111&_pii=S0021869316302873&_rdoc=1&_issn=00218693&md5=6f62ed0002316ca6e6358ef5be39b65d" title="Click to view the MathML source">Kclass="mathContainer hidden">class="mathCode">$\mathbb{K}$-automorphisms of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316302873&_mathId=si377.gif&_user=111111111&_pii=S0021869316302873&_rdoc=1&_issn=00218693&md5=5ae21c3b00cd2390d4f37ede78093750" title="Click to view the MathML source">K[X,Y,Z]/(f(X)Y−φ(Z))class="mathContainer hidden">class="mathCode">$\mathbb{K}[X,Y,Z]/(f(X)Y-\phi (Z))$ also for a specific choice of polynomials f and φ.