Affiliation:
1. 1. Dipartimento di Matematica “U. Dini”, Viale Morgagni 67/a, 50134 Firenze, Italy.
2. 2. Dipartimento di Matematica e Applicazioni per l'Architettura, Via dell'Agnolo 14, 50122 Firenze, Italy.
Abstract
Abstract
Let D(n, s, k) = {z∈ ℂ
n
: ( –|z
1|2 + |z
2|2)
k
+ ∑
i
s
=3 |zi
|2 – ∑
i
n
=
s
+1 |zi
|2 < 1}, where k ∈ ℤ+, 3 ≤ s ≤ n, and let M(n, s, k) = ∂D(n, s, k). We determine for any values of n, s and k the biholomorphic automorphisms of D(n, s, k), identifying, in suitable cases, the germs of biholomorphisms that map M(n, s, k) and D(n, s, k) respectively in themselves. It turns out that, if k is even and s = n, any such germ extends to a biholomorphic automorphism of D(n, s, k), while, in other cases, it is a branch of an algebraic correspondence.