Holomorphic maps from rational homogeneous spaces onto projective manifolds

TL;DR

This paper generalizes a previous result by showing that surjective holomorphic maps from higher Picard number rational homogeneous spaces onto projective manifolds are biholomorphisms, extending the understanding of such mappings.

Contribution

It extends Lazarsfeld, Hwang, and Mok's result to irreducible rational homogeneous spaces with higher Picard numbers, broadening the class of spaces where biholomorphicity is guaranteed.

Findings

Surjective holomorphic maps are biholomorphisms for higher Picard number spaces

Generalization of previous results to a broader class of homogeneous spaces

Enhanced understanding of morphisms between complex algebraic varieties

Abstract

Answering a problem raised by Lazarsfeld, Hwang and Mok proved that a surjective holomorphic map from a rational homogeneous space of Picard number 1 onto projective manifold different from projective space must be a biholomorphism. THe aim of this paper is to generalized this result to irreducible rational homogeneous space of higher Picard number.