Birational equivalence of the Zassenhaus varieties for basic classical Lie superalgebras and their purely-even reductive Lie subalgebras in odd characteristic

Let g=g(0)circle plus g(1) be a basic classical Lie superalgebra over an algebraically closed field k of characteristic p>2 . Denote by Z the center of the universal enveloping algebra U(g) . Then Z turns out to be finitely-generated purely-even commutative algebra without nonzero divisors. In this paper, we demonstrate that the fraction Frac(Z) is isomorphic to Frac(Z) for the center Z of U(g(0)) . Consequently, both Zassenhaus varieties for g and g(0) are birationally equivalent via a subalgebra Z subset of Z , and Spec(Z) is rational under the standard hypotheses.