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"> 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"> 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"> 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"> 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">-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"> also for a specific choice of polynomials f and φ.