New examples of proper holomorphic maps among symmetric domains

Rigidity of proper holomorphic maps between type-$\mathrm{I}$ irreducible bounded symmetric domains

“…In [11], Seo also pointed out the following fact regarding equivalence class of fibralimage-preserving maps and the corresponding moduli maps. Lemma 6.4 (cf.…”

“…We can then deduce from the maximum principle and the homogeneity of the domains that F 21 (Z) ≡ 0 (cf. [9,11]). Hence, we have…”

Proper holomorphic polynomial maps between bounded symmetric domains of classical type

“…We use Theorem 1.1 to prove that proper holomorphic maps f t : Ω 1 → Ω 2 are inequivalent for each 0 ≤ t ≤ 1. Every example in this section is obtained in [19]. As in [6], we define the following equivalence relation: Let Ω 1 , Ω 2 be domains.…”

“…If the difference of the ranks of the domains gets bigger, then it is expected that there are lots of inequivalent proper holomorphic maps. In [19], one way of finding proper holomorphic maps between bounded symmetric domains of type I is suggested and several proper holomorphic maps are constructed. For example, for r ′ = 2r − 1 and s ′ = 2s − 1, there is a generalized Whitney map defined by…”

“…In[19], there are generalizations of f 0 , f 1 tof 0 ,f 1 as proper holomorphic mapsf 0 : Ω I r,s → Ω I 2r−1,2s−1 andf 1 : Ω I r,s → Ω I…”