TY - JOUR

T1 - On local holomorphic maps preserving invariant (p; P)-forms between bounded symmetric domains

AU - Yuan, Yuan

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2017

Y1 - 2017

N2 - Let D; Ω1;Ω m be irreducible bounded symmetric domains.We study local holomorphic maps from D into Ω1Ω m preserving the in-variant (p; p)-forms induced from the normalized Bergman metrics up to conformal constants. We show that the local holomorphic maps extends to algebraic maps in the rank one case for any p and in the rank at least two case for certain sufficiently large p. The total geodesy thus follows if D = Bn; i = BNi for any p or if D = 1 = m with rank(D) 2 and p sufficiently large. As a consequence, the algebraic correspondence between quasi-projective varieties D= preserving invariant (p; p)-forms is modular, where is a torsion free, discrete, finite co-volume subgroup of Aut(D).

AB - Let D; Ω1;Ω m be irreducible bounded symmetric domains.We study local holomorphic maps from D into Ω1Ω m preserving the in-variant (p; p)-forms induced from the normalized Bergman metrics up to conformal constants. We show that the local holomorphic maps extends to algebraic maps in the rank one case for any p and in the rank at least two case for certain sufficiently large p. The total geodesy thus follows if D = Bn; i = BNi for any p or if D = 1 = m with rank(D) 2 and p sufficiently large. As a consequence, the algebraic correspondence between quasi-projective varieties D= preserving invariant (p; p)-forms is modular, where is a torsion free, discrete, finite co-volume subgroup of Aut(D).

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U2 - 10.4310/mrl.2017.v24.n6.a15

DO - 10.4310/mrl.2017.v24.n6.a15

M3 - Article

AN - SCOPUS:85041849794

SN - 1073-2780

VL - 24

SP - 1875

EP - 1895

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 6

ER -