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# A Coincidence Theorem for Holomorphic Maps to $G/P$

Published:2003-06-01
Printed: Jun 2003
• Parameswaran Sankaran
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## Abstract

The purpose of this note is to extend to an arbitrary generalized Hopf and Calabi-Eckmann manifold the following result of Kalyan Mukherjea: Let $V_n = \mathbb{S}^{2n+1} \times \mathbb{S}^{2n+1}$ denote a Calabi-Eckmann manifold. If $f,g \colon V_n \longrightarrow \mathbb{P}^n$ are any two holomorphic maps, at least one of them being non-constant, then there exists a coincidence: $f(x)=g(x)$ for some $x\in V_n$. Our proof involves a coincidence theorem for holomorphic maps to complex projective varieties of the form $G/P$ where $G$ is complex simple algebraic group and $P\subset G$ is a maximal parabolic subgroup, where one of the maps is dominant.
 MSC Classifications: 32H02 - Holomorphic mappings, (holomorphic) embeddings and related questions 54M20 - unknown classification 54M20

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