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

Let g = g0¯ ⊕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 (3) for the center 3 of U(g0¯). Consequently, both Zassenhaus varieties for g and g0¯ are birationally equivalent via a subalgebra Z¯⊂Z, and Spec (Z) is rational under the standard hypotheses.