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

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Abstract

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).

Original languageEnglish (US)
Pages (from-to)1875-1895
Number of pages21
JournalMathematical Research Letters
Volume24
Issue number6
DOIs
StatePublished - 2017

ASJC Scopus subject areas

  • Mathematics(all)

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